From 3ca88a8db18215f4b70aa17570dfde0d8c6fb1c6 Mon Sep 17 00:00:00 2001
From: Alexander Hess <alexander@webartifex.biz>
Date: Mon, 16 Mar 2020 20:51:51 +0100
Subject: [PATCH] Streamline presentation

---
 01_elements_00_lecture.ipynb  |   26 +-
 04_iteration_00_lecture.ipynb |    2 +-
 05_numbers_00_lecture.ipynb   | 2627 ++++++++++++++++++---------------
 3 files changed, 1463 insertions(+), 1192 deletions(-)

diff --git a/01_elements_00_lecture.ipynb b/01_elements_00_lecture.ipynb
index f7583ba..89beede 100644
--- a/01_elements_00_lecture.ipynb
+++ b/01_elements_00_lecture.ipynb
@@ -1308,7 +1308,7 @@
     }
    },
    "source": [
-    "The `c` object is a so-called **string** type (i.e., `str`), which is Python's way of representing \"text.\" Strings also come with peculiar behaviors, for example, to convert a text to lower, upper, or title case."
+    "The `c` object is a so-called **string** type (i.e., `str`), which is Python's way of representing \"text.\" Strings also come with peculiar behaviors, for example, to make a text lower or upper case."
    ]
   },
   {
@@ -1383,30 +1383,6 @@
     "c.upper()"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'Python Rocks'"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "c.title()"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {
diff --git a/04_iteration_00_lecture.ipynb b/04_iteration_00_lecture.ipynb
index fb89130..61858c5 100644
--- a/04_iteration_00_lecture.ipynb
+++ b/04_iteration_00_lecture.ipynb
@@ -52,7 +52,7 @@
    "cell_type": "markdown",
    "metadata": {
     "slideshow": {
-     "slide_type": "-"
+     "slide_type": "slide"
     }
    },
    "source": [
diff --git a/05_numbers_00_lecture.ipynb b/05_numbers_00_lecture.ipynb
index e4bed12..771a0ad 100644
--- a/05_numbers_00_lecture.ipynb
+++ b/05_numbers_00_lecture.ipynb
@@ -29,7 +29,7 @@
     "\n",
     "- [Chapter 1](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/01_elements_00_lecture.ipynb#%28Data%29-Type-%2F-%22Behavior%22) reveals that numbers may come in *different* data types (i.e., `int` vs. `float` so far),\n",
     "- [Chapter 3](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/03_conditionals_00_lecture.ipynb#Boolean-Expressions) raises questions regarding the **limited precision** of `float` numbers (e.g., `42 == 42.000000000000001` evaluates to `True`), and\n",
-    "- [Chapter 4](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/04_iteration_00_lecture.ipynb#Infinite-Recursion) shows that sometimes a `float` \"walks\" and \"quacks\" like an `int`, whereas the reverse is true in other cases.\n",
+    "- [Chapter 4](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/04_iteration_00_lecture.ipynb#Infinite-Recursion) shows that sometimes a `float` \"walks\" and \"quacks\" like an `int`, whereas the reverse is true.\n",
     "\n",
     "This chapter introduces all the [built-in numeric types](https://docs.python.org/3/library/stdtypes.html#numeric-types-int-float-complex): `int`, `float`, and `complex`. To mitigate the limited precision of floating-point numbers, we also look at two replacements for the `float` type in the [standard library](https://docs.python.org/3/library/index.html), namely the `Decimal` type in the [decimals](https://docs.python.org/3/library/decimal.html#decimal.Decimal) and the `Fraction` type in the [fractions](https://docs.python.org/3/library/fractions.html#fractions.Fraction) module."
    ]
@@ -53,7 +53,9 @@
     }
    },
    "source": [
-    "The simplest numeric type is the `int` type: It behaves like an [integer in ordinary math](https://en.wikipedia.org/wiki/Integer) (i.e., the set $\\mathbb{Z}$) and supports operators in the way we saw in the section on arithmetic operators in [Chapter 1](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/01_elements_00_lecture.ipynb#%28Arithmetic%29-Operators)."
+    "The simplest numeric type is the `int` type: It behaves like an [integer in ordinary math](https://en.wikipedia.org/wiki/Integer) (i.e., the set $\\mathbb{Z}$) and supports operators in the way we saw in the section on arithmetic operators in [Chapter 1](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/01_elements_00_lecture.ipynb#%28Arithmetic%29-Operators).\n",
+    "\n",
+    "One way to create `int` objects is by simply writing its value as a literal with the digits `0` to `9`."
    ]
   },
   {
@@ -92,7 +94,7 @@
     {
      "data": {
       "text/plain": [
-       "94315929536576"
+       "94784085682240"
       ]
      },
      "execution_count": 2,
@@ -160,7 +162,7 @@
     }
    },
    "source": [
-    "A nice feature in newer Python versions is using underscores `_` as (thousands) separators in numeric literals. For example, `1_000_000` evaluates to `1000000` in memory; the `_` is simply ignored by the interpreter."
+    "A nice feature in newer Python versions is using underscores `_` as (thousands) separators in numeric literals. For example, `1_000_000` evaluates to `1000000` in memory; the `_` is ignored by the interpreter."
    ]
   },
   {
@@ -195,7 +197,7 @@
     }
    },
    "source": [
-    "The `int` type follows all rules we know from math, apart from one exception: Whereas mathematicians argue what the term $0^0$ means (cf., this [article](https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero)), programmers are pragmatic about this and define $0^0 = 1$."
+    "We may place the `_`s anywhere we want."
    ]
   },
   {
@@ -210,7 +212,7 @@
     {
      "data": {
       "text/plain": [
-       "1"
+       "123456789"
       ]
      },
      "execution_count": 6,
@@ -218,6 +220,252 @@
      "output_type": "execute_result"
     }
    ],
+   "source": [
+    "1_2_3_4_5_6_7_8_9"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "It is syntactically invalid to write out leading `0` in numeric literals. The reason for that will become apparent in the next section."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "ename": "SyntaxError",
+     "evalue": "invalid token (<ipython-input-7-9a7f0f99e867>, line 1)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-7-9a7f0f99e867>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    042\u001b[0m\n\u001b[0m      ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid token\n"
+     ]
+    }
+   ],
+   "source": [
+    "042"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "Another way to create `int` objects is with the [int()](https://docs.python.org/3/library/functions.html#int) built-in that casts `float` or properly formatted `str` objects as integers. So, decimals are truncated (i.e., \"cut off\")."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "int(42.11)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "int(42.87)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "Whereas the floor division operator `//` effectively rounds towards negative infinity (cf., the \"*(Arithmetic) Operators*\" section in [Chapter 1](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/01_elements_00_lecture.ipynb#%28Arithmetic%29-Operators)), the [int()](https://docs.python.org/3/library/functions.html#int) built-in effectively rounds towards `0`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-42"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "int(-42.87)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "When casting `str` objects as `int`, the [int()](https://docs.python.org/3/library/functions.html#int) built-in is less forgiving. We must not include any decimals as shows by the `ValueError`. Yet, leading and trailing whitespace is gracefully ignored."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "int(\"42\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "ename": "ValueError",
+     "evalue": "invalid literal for int() with base 10: '42.0'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-12-faae6b054331>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"42.0\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;31mValueError\u001b[0m: invalid literal for int() with base 10: '42.0'"
+     ]
+    }
+   ],
+   "source": [
+    "int(\"42.0\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "int(\" 42 \")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "The `int` type follows all rules we know from math, apart from one exception: Whereas mathematicians to this day argue what the term $0^0$ means (cf., this [article](https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero)), programmers are pragmatic about this and simply define $0^0 = 1$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "0 ** 0"
    ]
@@ -277,7 +525,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 15,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -290,7 +538,7 @@
        "'0b11'"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -312,7 +560,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 16,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -325,7 +573,7 @@
        "3"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -347,7 +595,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 17,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -360,7 +608,7 @@
        "3"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -382,7 +630,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 18,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -395,7 +643,7 @@
        "3"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -417,7 +665,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 19,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -430,7 +678,7 @@
        "'0b1111011'"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -452,7 +700,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 20,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -465,7 +713,7 @@
        "123"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -487,7 +735,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 21,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -500,7 +748,7 @@
        "'0b0'"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -511,7 +759,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 22,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -524,7 +772,7 @@
        "'0b1'"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -535,7 +783,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 23,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -548,7 +796,7 @@
        "'0b10'"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -559,7 +807,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 24,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -572,7 +820,7 @@
        "'0b11111111'"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -596,7 +844,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 25,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -609,7 +857,7 @@
        "'0b1100010101'"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -660,7 +908,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 26,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -673,7 +921,7 @@
        "3"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -684,7 +932,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 27,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -697,7 +945,7 @@
        "'0b1 + 0b10 = 0b11'"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -719,7 +967,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 28,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -732,7 +980,7 @@
        "4"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -743,7 +991,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 29,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -756,7 +1004,7 @@
        "'0b1 + 0b11 = 0b100'"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -778,7 +1026,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 30,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -791,7 +1039,7 @@
        "12"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -802,7 +1050,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 31,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -815,7 +1063,7 @@
        "'0b100 * 0b11 = 0b1100'"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -826,7 +1074,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 32,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -839,7 +1087,7 @@
        "'0b100 * 0b1 = 0b100'"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -850,7 +1098,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 33,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -863,7 +1111,7 @@
        "'0b100 * 0b10 = 0b1000'"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -958,7 +1206,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 34,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -971,7 +1219,7 @@
        "'0x0'"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -982,7 +1230,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 35,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -995,7 +1243,7 @@
        "'0x1'"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1017,7 +1265,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 36,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1030,7 +1278,7 @@
        "'0x3'"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1052,7 +1300,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 37,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1065,7 +1313,7 @@
        "'0xa'"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1076,7 +1324,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 38,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1089,7 +1337,7 @@
        "'0xf'"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1111,7 +1359,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 39,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -1124,7 +1372,7 @@
        "'0b1111011'"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1135,7 +1383,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 40,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1148,7 +1396,7 @@
        "'0x7b'"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 40,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1170,7 +1418,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 41,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1183,7 +1431,7 @@
        "123"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 41,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1205,7 +1453,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 42,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1218,7 +1466,7 @@
        "123"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 42,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1240,7 +1488,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 43,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1253,7 +1501,7 @@
        "'0x0'"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 43,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1264,7 +1512,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 44,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1277,7 +1525,7 @@
        "'0xff'"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 44,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1299,7 +1547,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 45,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1312,7 +1560,7 @@
        "'0x315'"
       ]
      },
-     "execution_count": 37,
+     "execution_count": 45,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1358,7 +1606,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 46,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1371,7 +1619,7 @@
        "'-0b11'"
       ]
      },
-     "execution_count": 38,
+     "execution_count": 46,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1382,7 +1630,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 47,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1395,7 +1643,7 @@
        "'-0x3'"
       ]
      },
-     "execution_count": 39,
+     "execution_count": 47,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1406,7 +1654,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 48,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1419,7 +1667,7 @@
        "'-0b11111111'"
       ]
      },
-     "execution_count": 40,
+     "execution_count": 48,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1430,7 +1678,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 49,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1443,7 +1691,7 @@
        "'-0xff'"
       ]
      },
-     "execution_count": 41,
+     "execution_count": 49,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1476,7 +1724,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 50,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -1489,7 +1737,7 @@
        "1"
       ]
      },
-     "execution_count": 42,
+     "execution_count": 50,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1500,7 +1748,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 51,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1513,7 +1761,7 @@
        "42"
       ]
      },
-     "execution_count": 43,
+     "execution_count": 51,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1524,7 +1772,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 52,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1537,7 +1785,7 @@
        "0.0"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 52,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1559,7 +1807,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 53,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -1572,7 +1820,7 @@
        "1"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 53,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1583,7 +1831,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 54,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1596,7 +1844,7 @@
        "0"
       ]
      },
-     "execution_count": 46,
+     "execution_count": 54,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1618,7 +1866,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 55,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -1631,7 +1879,7 @@
        "'0b1'"
       ]
      },
-     "execution_count": 47,
+     "execution_count": 55,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1642,7 +1890,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 56,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1655,7 +1903,7 @@
        "'0b0'"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 56,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1677,7 +1925,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 57,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1690,7 +1938,7 @@
        "'0x1'"
       ]
      },
-     "execution_count": 49,
+     "execution_count": 57,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1701,7 +1949,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 58,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -1714,7 +1962,7 @@
        "'0x0'"
       ]
      },
-     "execution_count": 50,
+     "execution_count": 58,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1736,7 +1984,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 59,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -1750,7 +1998,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-51-af2123a46eb2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-59-af2123a46eb2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m: int() argument must be a string, a bytes-like object or a number, not 'NoneType'"
      ]
     }
@@ -1787,7 +2035,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 60,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -1800,7 +2048,7 @@
        "9"
       ]
      },
-     "execution_count": 52,
+     "execution_count": 60,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1811,7 +2059,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 61,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1824,7 +2072,7 @@
        "'0b1011 & 0b1101'"
       ]
      },
-     "execution_count": 53,
+     "execution_count": 61,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1835,7 +2083,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 62,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1848,7 +2096,7 @@
        "'0b1001'"
       ]
      },
-     "execution_count": 54,
+     "execution_count": 62,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1870,7 +2118,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 63,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1883,7 +2131,7 @@
        "9"
       ]
      },
-     "execution_count": 55,
+     "execution_count": 63,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1905,7 +2153,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 64,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -1918,7 +2166,7 @@
        "13"
       ]
      },
-     "execution_count": 56,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1929,7 +2177,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 65,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1942,7 +2190,7 @@
        "'0b1001 | 0b1101'"
       ]
      },
-     "execution_count": 57,
+     "execution_count": 65,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1953,7 +2201,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 66,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1966,7 +2214,7 @@
        "'0b1101'"
       ]
      },
-     "execution_count": 58,
+     "execution_count": 66,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1988,7 +2236,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 67,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2001,7 +2249,7 @@
        "13"
       ]
      },
-     "execution_count": 59,
+     "execution_count": 67,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2023,7 +2271,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 68,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -2036,7 +2284,7 @@
        "4"
       ]
      },
-     "execution_count": 60,
+     "execution_count": 68,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2047,7 +2295,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 69,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2060,7 +2308,7 @@
        "'0b1001 ^ 0b1101'"
       ]
      },
-     "execution_count": 61,
+     "execution_count": 69,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2071,7 +2319,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 70,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2084,7 +2332,7 @@
        "'0b100'"
       ]
      },
-     "execution_count": 62,
+     "execution_count": 70,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2106,7 +2354,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 71,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2119,7 +2367,7 @@
        "4"
       ]
      },
-     "execution_count": 63,
+     "execution_count": 71,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2143,7 +2391,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 72,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -2156,7 +2404,7 @@
        "-8"
       ]
      },
-     "execution_count": 64,
+     "execution_count": 72,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2167,7 +2415,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 73,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2180,7 +2428,7 @@
        "True"
       ]
      },
-     "execution_count": 65,
+     "execution_count": 73,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2191,7 +2439,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 66,
+   "execution_count": 74,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2204,7 +2452,7 @@
        "'-0b1000'"
       ]
      },
-     "execution_count": 66,
+     "execution_count": 74,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2215,7 +2463,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 67,
+   "execution_count": 75,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2228,7 +2476,7 @@
        "'-0b1000'"
       ]
      },
-     "execution_count": 67,
+     "execution_count": 75,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2250,7 +2498,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 68,
+   "execution_count": 76,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -2263,7 +2511,7 @@
        "-1"
       ]
      },
-     "execution_count": 68,
+     "execution_count": 76,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2287,7 +2535,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 77,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -2300,7 +2548,7 @@
        "28"
       ]
      },
-     "execution_count": 69,
+     "execution_count": 77,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2311,7 +2559,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 78,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2324,7 +2572,7 @@
        "'0b111'"
       ]
      },
-     "execution_count": 70,
+     "execution_count": 78,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2335,7 +2583,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 79,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2348,7 +2596,7 @@
        "'0b11100'"
       ]
      },
-     "execution_count": 71,
+     "execution_count": 79,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2359,7 +2607,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 80,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2372,7 +2620,7 @@
        "28"
       ]
      },
-     "execution_count": 72,
+     "execution_count": 80,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2394,7 +2642,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 81,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -2407,7 +2655,7 @@
        "3"
       ]
      },
-     "execution_count": 73,
+     "execution_count": 81,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2418,7 +2666,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 74,
+   "execution_count": 82,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2431,7 +2679,7 @@
        "'0b111'"
       ]
      },
-     "execution_count": 74,
+     "execution_count": 82,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2442,7 +2690,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 83,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2455,7 +2703,7 @@
        "'0b11'"
       ]
      },
-     "execution_count": 75,
+     "execution_count": 83,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2466,7 +2714,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 84,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2479,7 +2727,7 @@
        "3"
       ]
      },
-     "execution_count": 76,
+     "execution_count": 84,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2518,7 +2766,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 77,
+   "execution_count": 85,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -2531,7 +2779,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
+   "execution_count": 86,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2541,10 +2789,10 @@
     {
      "data": {
       "text/plain": [
-       "139674754277776"
+       "139663468493296"
       ]
      },
-     "execution_count": 78,
+     "execution_count": 86,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2555,7 +2803,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": 87,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2568,272 +2816,13 @@
        "float"
       ]
      },
-     "execution_count": 79,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "type(b)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "42.0"
-      ]
-     },
-     "execution_count": 80,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "b"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "As with integer literals above, we may use underscores `_` to make longer `float` objects easier to read."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0.123456789"
-      ]
-     },
-     "execution_count": 81,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "0.123_456_789"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "In cases where the dot `.` is unnecessary from a mathematical point of view, we either need to end the number with it nevertheless or use the [float()](https://docs.python.org/3/library/functions.html#float) built-in to cast the number explicitly. [float()](https://docs.python.org/3/library/functions.html#float) can process any numeric object or a properly formatted `str` object."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "42.0"
-      ]
-     },
-     "execution_count": 82,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "42."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "42.0"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(42)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "42.0"
-      ]
-     },
-     "execution_count": 84,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\"42\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "Leading and trailing whitespace is ignored ..."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "42.87"
-      ]
-     },
-     "execution_count": 85,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\" 42.87 \")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "... but not whitespace in between."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "ename": "ValueError",
-     "evalue": "could not convert string to float: '42. 87'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-86-c7953b8b7956>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"42. 87\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;31mValueError\u001b[0m: could not convert string to float: '42. 87'"
-     ]
-    }
-   ],
-   "source": [
-    "float(\"42. 87\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "`float` objects are implicitly created as the result of dividing an `int` object by another with the division operator `/`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0.3333333333333333"
-      ]
-     },
      "execution_count": 87,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "1 / 3"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "In general, if we combine `float` and `int` objects in arithmetic operations, we always end up with a `float` type: Python uses the \"broader\" representation."
+    "type(b)"
    ]
   },
   {
@@ -2857,12 +2846,82 @@
     }
    ],
    "source": [
-    "40.0 + 2"
+    "b"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "As with integer literals above, we may use underscores `_` to make longer `float` objects easier to read."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 89,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.123456789"
+      ]
+     },
+     "execution_count": 89,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "0.123_456_789"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "In cases where the dot `.` is unnecessary from a mathematical point of view, we either need to end the number with it nevertheless or use the [float()](https://docs.python.org/3/library/functions.html#float) built-in to cast the number explicitly. [float()](https://docs.python.org/3/library/functions.html#float) can process any numeric object or a properly formatted `str` object."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 90,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42.0"
+      ]
+     },
+     "execution_count": 90,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "42."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -2875,7 +2934,196 @@
        "42.0"
       ]
      },
-     "execution_count": 89,
+     "execution_count": 91,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(42)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42.0"
+      ]
+     },
+     "execution_count": 92,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(\"42\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "Leading and trailing whitespace is ignored ..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42.87"
+      ]
+     },
+     "execution_count": 93,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(\" 42.87 \")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "... but not whitespace in between."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "ename": "ValueError",
+     "evalue": "could not convert string to float: '42. 87'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-94-c7953b8b7956>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"42. 87\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;31mValueError\u001b[0m: could not convert string to float: '42. 87'"
+     ]
+    }
+   ],
+   "source": [
+    "float(\"42. 87\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "`float` objects are implicitly created as the result of dividing an `int` object by another with the division operator `/`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 95,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.3333333333333333"
+      ]
+     },
+     "execution_count": 95,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "1 / 3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "In general, if we combine `float` and `int` objects in arithmetic operations, we always end up with a `float` type: Python uses the \"broader\" representation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 96,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42.0"
+      ]
+     },
+     "execution_count": 96,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "40.0 + 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "42.0"
+      ]
+     },
+     "execution_count": 97,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2908,7 +3156,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 90,
+   "execution_count": 98,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -2921,7 +3169,7 @@
        "1.23"
       ]
      },
-     "execution_count": 90,
+     "execution_count": 98,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2943,7 +3191,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 91,
+   "execution_count": 99,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -2952,10 +3200,10 @@
    "outputs": [
     {
      "ename": "SyntaxError",
-     "evalue": "invalid syntax (<ipython-input-91-1b5daaac0077>, line 1)",
+     "evalue": "invalid syntax (<ipython-input-99-1b5daaac0077>, line 1)",
      "output_type": "error",
      "traceback": [
-      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-91-1b5daaac0077>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    1.23 e0\u001b[0m\n\u001b[0m          ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-99-1b5daaac0077>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    1.23 e0\u001b[0m\n\u001b[0m          ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
      ]
     }
    ],
@@ -2965,7 +3213,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 92,
+   "execution_count": 100,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -2974,10 +3222,10 @@
    "outputs": [
     {
      "ename": "SyntaxError",
-     "evalue": "invalid syntax (<ipython-input-92-a236c4a30231>, line 1)",
+     "evalue": "invalid syntax (<ipython-input-100-a236c4a30231>, line 1)",
      "output_type": "error",
      "traceback": [
-      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-92-a236c4a30231>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    1.23e 0\u001b[0m\n\u001b[0m        ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-100-a236c4a30231>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    1.23e 0\u001b[0m\n\u001b[0m        ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
      ]
     }
    ],
@@ -2987,7 +3235,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 93,
+   "execution_count": 101,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -2996,10 +3244,10 @@
    "outputs": [
     {
      "ename": "SyntaxError",
-     "evalue": "invalid syntax (<ipython-input-93-05b9072d76be>, line 1)",
+     "evalue": "invalid syntax (<ipython-input-101-05b9072d76be>, line 1)",
      "output_type": "error",
      "traceback": [
-      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-93-05b9072d76be>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    1.23e0.0\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-101-05b9072d76be>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    1.23e0.0\u001b[0m\n\u001b[0m           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
      ]
     }
    ],
@@ -3020,7 +3268,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 94,
+   "execution_count": 102,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -3034,7 +3282,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-94-abc4de6ccb5e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0me0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-102-abc4de6ccb5e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0me0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mNameError\u001b[0m: name 'e0' is not defined"
      ]
     }
@@ -3056,7 +3304,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 95,
+   "execution_count": 103,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3069,7 +3317,7 @@
        "1.0"
       ]
      },
-     "execution_count": 95,
+     "execution_count": 103,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3091,7 +3339,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 96,
+   "execution_count": 104,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3104,7 +3352,7 @@
        "1000.0"
       ]
      },
-     "execution_count": 96,
+     "execution_count": 104,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3126,7 +3374,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 97,
+   "execution_count": 105,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3139,7 +3387,7 @@
        "0.001"
       ]
      },
-     "execution_count": 97,
+     "execution_count": 105,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3170,255 +3418,19 @@
     "There are also three special values representing \"**not a number,**\" called `nan`, and positive or negative **infinity**, called `inf` or `-inf`, that are created by passing in the corresponding abbreviation as a `str` object to the [float()](https://docs.python.org/3/library/functions.html#float) built-in. These values could be used, for example, as the result of a mathematically undefined operation like division by zero or to model the value of a mathematical function as it goes to infinity."
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "nan"
-      ]
-     },
-     "execution_count": 98,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\"nan\")  # also float(\"NaN\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "inf"
-      ]
-     },
-     "execution_count": 99,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\"+inf\")  # also float(\"+infinity\") or float(\"infinity\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "inf"
-      ]
-     },
-     "execution_count": 100,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\"inf\")  # same as float(\"+inf\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "-inf"
-      ]
-     },
-     "execution_count": 101,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\"-inf\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "`nan` objects *never* compare equal to *anything*, not even to themselves. This happens in accordance with the [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "False"
-      ]
-     },
-     "execution_count": 102,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\"nan\") == float(\"nan\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "Another caveat is that any arithmetic involving a `nan` object results in `nan`. In other words, the addition below **fails silently** as no error is raised. As this also happens in accordance with the [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard, we *need* to be aware of that and check any data we work with for any `nan` occurrences *before* doing any calculations."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "nan"
-      ]
-     },
-     "execution_count": 103,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "42 + float(\"nan\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "On the contrary, as two values go to infinity, there is no such concept as difference and *everything* compares equal."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\"inf\") == float(\"inf\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "Adding `42` to `inf` makes no difference."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "inf"
-      ]
-     },
-     "execution_count": 105,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "float(\"inf\") + 42"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 106,
    "metadata": {
     "slideshow": {
-     "slide_type": "fragment"
+     "slide_type": "slide"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "True"
+       "nan"
       ]
      },
      "execution_count": 106,
@@ -3427,18 +3439,7 @@
     }
    ],
    "source": [
-    "float(\"inf\") + 42 == float(\"inf\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "We observe the same for multiplication ..."
+    "float(\"nan\")  # also float(\"NaN\")"
    ]
   },
   {
@@ -3462,12 +3463,259 @@
     }
    ],
    "source": [
-    "42 * float(\"inf\")"
+    "float(\"+inf\")  # also float(\"+infinity\") or float(\"infinity\")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 108,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "inf"
+      ]
+     },
+     "execution_count": 108,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(\"inf\")  # same as float(\"+inf\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 109,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-inf"
+      ]
+     },
+     "execution_count": 109,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(\"-inf\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "`nan` objects *never* compare equal to *anything*, not even to themselves. This happens in accordance with the [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 110,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 110,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(\"nan\") == float(\"nan\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "Another caveat is that any arithmetic involving a `nan` object results in `nan`. In other words, the addition below **fails silently** as no error is raised. As this also happens in accordance with the [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard, we *need* to be aware of that and check any data we work with for any `nan` occurrences *before* doing any calculations."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 111,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "nan"
+      ]
+     },
+     "execution_count": 111,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "42 + float(\"nan\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "On the contrary, as two values go to infinity, there is no such concept as difference and *everything* compares equal."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 112,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 112,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(\"inf\") == float(\"inf\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "Adding `42` to `inf` makes no difference."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 113,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "inf"
+      ]
+     },
+     "execution_count": 113,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(\"inf\") + 42"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 114,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 114,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "float(\"inf\") + 42 == float(\"inf\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "We observe the same for multiplication ..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 115,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "inf"
+      ]
+     },
+     "execution_count": 115,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "42 * float(\"inf\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 116,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -3480,7 +3728,7 @@
        "True"
       ]
      },
-     "execution_count": 108,
+     "execution_count": 116,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3502,7 +3750,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 109,
+   "execution_count": 117,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -3515,7 +3763,7 @@
        "inf"
       ]
      },
-     "execution_count": 109,
+     "execution_count": 117,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3526,7 +3774,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 110,
+   "execution_count": 118,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -3539,7 +3787,7 @@
        "True"
       ]
      },
-     "execution_count": 110,
+     "execution_count": 118,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3561,7 +3809,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 111,
+   "execution_count": 119,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -3574,7 +3822,7 @@
        "inf"
       ]
      },
-     "execution_count": 111,
+     "execution_count": 119,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3585,7 +3833,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 112,
+   "execution_count": 120,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3598,7 +3846,7 @@
        "True"
       ]
      },
-     "execution_count": 112,
+     "execution_count": 120,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3620,7 +3868,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 113,
+   "execution_count": 121,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -3633,7 +3881,7 @@
        "nan"
       ]
      },
-     "execution_count": 113,
+     "execution_count": 121,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3644,7 +3892,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 114,
+   "execution_count": 122,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3657,7 +3905,7 @@
        "nan"
       ]
      },
-     "execution_count": 114,
+     "execution_count": 122,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3692,7 +3940,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 115,
+   "execution_count": 123,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -3705,7 +3953,7 @@
        "1000000000000001.0"
       ]
      },
-     "execution_count": 115,
+     "execution_count": 123,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3716,7 +3964,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 116,
+   "execution_count": 124,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3729,7 +3977,7 @@
        "1e+16"
       ]
      },
-     "execution_count": 116,
+     "execution_count": 124,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3751,7 +3999,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 117,
+   "execution_count": 125,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -3764,7 +4012,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 118,
+   "execution_count": 126,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3777,7 +4025,7 @@
        "2.0000000000000004"
       ]
      },
-     "execution_count": 118,
+     "execution_count": 126,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3788,7 +4036,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 119,
+   "execution_count": 127,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3801,7 +4049,7 @@
        "0.30000000000000004"
       ]
      },
-     "execution_count": 119,
+     "execution_count": 127,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3823,7 +4071,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 120,
+   "execution_count": 128,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3836,7 +4084,7 @@
        "False"
       ]
      },
-     "execution_count": 120,
+     "execution_count": 128,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3847,7 +4095,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 121,
+   "execution_count": 129,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3860,7 +4108,7 @@
        "False"
       ]
      },
-     "execution_count": 121,
+     "execution_count": 129,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3882,7 +4130,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 122,
+   "execution_count": 130,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -3895,7 +4143,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 123,
+   "execution_count": 131,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3908,7 +4156,7 @@
        "True"
       ]
      },
-     "execution_count": 123,
+     "execution_count": 131,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3919,7 +4167,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 124,
+   "execution_count": 132,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3932,7 +4180,7 @@
        "True"
       ]
      },
-     "execution_count": 124,
+     "execution_count": 132,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3949,14 +4197,14 @@
     }
    },
    "source": [
-    "The built-in [format()](https://docs.python.org/3/library/functions.html#format) function allows us to show the **significant digits** of a `float` number as they exist in memory to arbitrary precision. To exemplify it, let's view a couple of `float` objects with `50` digits. This analysis reveals that almost no `float` number is precise! After $14$ or $15$ digits \"weird\" things happen. As we see further below, the \"random\" digits ending the `float` numbers do *not* \"physically\" exist in memory.\n",
+    "The built-in [format()](https://docs.python.org/3/library/functions.html#format) function allows us to show the **significant digits** of a `float` number as they exist in memory to arbitrary precision. To exemplify it, let's view a couple of `float` objects with `50` digits. This analysis reveals that almost no `float` number is precise! After 14 or 15 digits \"weird\" things happen. As we see further below, the \"random\" digits ending the `float` numbers do *not* \"physically\" exist in memory! Rather, they are \"calculated\" by the [format()](https://docs.python.org/3/library/functions.html#format) function that is forced to show `50` digits.\n",
     "\n",
-    "The [format()](https://docs.python.org/3/library/functions.html#format) function is different from the [format()](https://docs.python.org/3/library/stdtypes.html#str.format) method on `str` objects introduced in the next chapter and both work with the so-called [format specification mini-language](https://docs.python.org/3/library/string.html#format-specification-mini-language): `\".50f\"` is the instruction to show `50` digits of a `float` number. But let's not worry too much about these details for now."
+    "The [format()](https://docs.python.org/3/library/functions.html#format) function is different from the [format()](https://docs.python.org/3/library/stdtypes.html#str.format) method on `str` objects introduced in the next chapter (cf., [Chapter 6](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/06_text_00_lecture.ipynb#format%28%29-Method)): Yet, both work with the so-called [format specification mini-language](https://docs.python.org/3/library/string.html#format-specification-mini-language): `\".50f\"` is the instruction to show `50` digits of a `float` number."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 125,
+   "execution_count": 133,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -3969,7 +4217,7 @@
        "'0.10000000000000000555111512312578270211815834045410'"
       ]
      },
-     "execution_count": 125,
+     "execution_count": 133,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3980,7 +4228,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 126,
+   "execution_count": 134,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3993,7 +4241,7 @@
        "'0.20000000000000001110223024625156540423631668090820'"
       ]
      },
-     "execution_count": 126,
+     "execution_count": 134,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4004,7 +4252,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 127,
+   "execution_count": 135,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4017,7 +4265,7 @@
        "'0.29999999999999998889776975374843459576368331909180'"
       ]
      },
-     "execution_count": 127,
+     "execution_count": 135,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4028,7 +4276,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 128,
+   "execution_count": 136,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4041,7 +4289,7 @@
        "'0.33333333333333331482961625624739099293947219848633'"
       ]
      },
-     "execution_count": 128,
+     "execution_count": 136,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4067,7 +4315,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 129,
+   "execution_count": 137,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4080,7 +4328,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 130,
+   "execution_count": 138,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4093,7 +4341,7 @@
        "0.33333"
       ]
      },
-     "execution_count": 130,
+     "execution_count": 138,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4104,7 +4352,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 131,
+   "execution_count": 139,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4117,7 +4365,7 @@
        "'0.33333000000000001517008740847813896834850311279297'"
       ]
      },
-     "execution_count": 131,
+     "execution_count": 139,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4139,7 +4387,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 132,
+   "execution_count": 140,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4152,7 +4400,7 @@
        "'0.12500000000000000000000000000000000000000000000000'"
       ]
      },
-     "execution_count": 132,
+     "execution_count": 140,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4163,7 +4411,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 133,
+   "execution_count": 141,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4176,7 +4424,7 @@
        "'0.25000000000000000000000000000000000000000000000000'"
       ]
      },
-     "execution_count": 133,
+     "execution_count": 141,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4187,7 +4435,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 134,
+   "execution_count": 142,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4200,7 +4448,7 @@
        "True"
       ]
      },
-     "execution_count": 134,
+     "execution_count": 142,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4287,7 +4535,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 135,
+   "execution_count": 143,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4300,7 +4548,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 136,
+   "execution_count": 144,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4313,7 +4561,7 @@
        "'0x1.0000000000000p-3'"
       ]
      },
-     "execution_count": 136,
+     "execution_count": 144,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4335,7 +4583,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 137,
+   "execution_count": 145,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4348,7 +4596,7 @@
        "(1, 8)"
       ]
      },
-     "execution_count": 137,
+     "execution_count": 145,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4359,7 +4607,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 138,
+   "execution_count": 146,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4372,7 +4620,7 @@
        "'0x1.555475a31a4bep-2'"
       ]
      },
-     "execution_count": 138,
+     "execution_count": 146,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4383,7 +4631,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 139,
+   "execution_count": 147,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4396,7 +4644,7 @@
        "(3002369727582815, 9007199254740992)"
       ]
      },
-     "execution_count": 139,
+     "execution_count": 147,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4418,7 +4666,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 140,
+   "execution_count": 148,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4431,7 +4679,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 141,
+   "execution_count": 149,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4444,7 +4692,7 @@
        "'0x0.0p+0'"
       ]
      },
-     "execution_count": 141,
+     "execution_count": 149,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4455,7 +4703,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 142,
+   "execution_count": 150,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4468,7 +4716,7 @@
        "(0, 1)"
       ]
      },
-     "execution_count": 142,
+     "execution_count": 150,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4490,7 +4738,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 143,
+   "execution_count": 151,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4503,7 +4751,7 @@
        "False"
       ]
      },
-     "execution_count": 143,
+     "execution_count": 151,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4514,7 +4762,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 144,
+   "execution_count": 152,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4527,7 +4775,7 @@
        "True"
       ]
      },
-     "execution_count": 144,
+     "execution_count": 152,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4551,7 +4799,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 145,
+   "execution_count": 153,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4564,7 +4812,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 146,
+   "execution_count": 154,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4577,7 +4825,7 @@
        "sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)"
       ]
      },
-     "execution_count": 146,
+     "execution_count": 154,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4612,7 +4860,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 147,
+   "execution_count": 155,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4636,7 +4884,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 148,
+   "execution_count": 156,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4649,7 +4897,7 @@
        "Context(prec=28, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999, capitals=1, clamp=0, flags=[], traps=[InvalidOperation, DivisionByZero, Overflow])"
       ]
      },
-     "execution_count": 148,
+     "execution_count": 156,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4669,242 +4917,6 @@
     "The two simplest ways to create a `Decimal` object is to either **instantiate** it with an `int` or a `str` object consisting of all the significant digits. In the latter case, the scientific notation is also possible."
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 149,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Decimal('42')"
-      ]
-     },
-     "execution_count": 149,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(42)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 150,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Decimal('0.1')"
-      ]
-     },
-     "execution_count": 150,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"0.1\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 151,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Decimal('0.001')"
-      ]
-     },
-     "execution_count": 151,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"1e-3\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "It is *not* a good idea to create a `Decimal` from a `float` object. If we did so, we would create a `Decimal` object that internally used extra bits to store the \"random\" digits that are not stored in the `float` object in the first place."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 152,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Decimal('0.1000000000000000055511151231257827021181583404541015625')"
-      ]
-     },
-     "execution_count": 152,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(0.1)  # do not do this"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "With the `Decimal` type, the imprecisions in the arithmetic and equality comparisons from above go away."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 153,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "slide"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Decimal('0.3')"
-      ]
-     },
-     "execution_count": 153,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"0.1\") + Decimal(\"0.2\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 154,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 154,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"0.1\") + Decimal(\"0.2\") == Decimal(\"0.3\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "`Decimal` numbers *preserve* the **significant digits**, even in cases where this is not needed."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 155,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "fragment"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Decimal('0.30000')"
-      ]
-     },
-     "execution_count": 155,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"0.10000\") + Decimal(\"0.20000\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 156,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 156,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"0.10000\") + Decimal(\"0.20000\") == Decimal(\"0.3\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "source": [
-    "Arithmetic operations between `Decimal` and `int` objects work as the latter are inherently precise: The results are *new* `Decimal` objects."
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": 157,
@@ -4926,7 +4938,7 @@
     }
    ],
    "source": [
-    "21 + Decimal(21)"
+    "Decimal(42)"
    ]
   },
   {
@@ -4941,7 +4953,7 @@
     {
      "data": {
       "text/plain": [
-       "Decimal('42.0')"
+       "Decimal('0.1')"
       ]
      },
      "execution_count": 158,
@@ -4949,13 +4961,249 @@
      "output_type": "execute_result"
     }
    ],
+   "source": [
+    "Decimal(\"0.1\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 159,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('0.001')"
+      ]
+     },
+     "execution_count": 159,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Decimal(\"1e-3\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "It is *not* a good idea to create a `Decimal` from a `float` object. If we did so, we would create a `Decimal` object that internally used extra bits to store the \"random\" digits that are not stored in the `float` object in the first place."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 160,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('0.1000000000000000055511151231257827021181583404541015625')"
+      ]
+     },
+     "execution_count": 160,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Decimal(0.1)  # do not do this"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "With the `Decimal` type, the imprecisions in the arithmetic and equality comparisons from above go away."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 161,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('0.3')"
+      ]
+     },
+     "execution_count": 161,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Decimal(\"0.1\") + Decimal(\"0.2\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 162,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 162,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Decimal(\"0.1\") + Decimal(\"0.2\") == Decimal(\"0.3\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "`Decimal` numbers *preserve* the **significant digits**, even in cases where this is not needed."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 163,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('0.30000')"
+      ]
+     },
+     "execution_count": 163,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Decimal(\"0.10000\") + Decimal(\"0.20000\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 164,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 164,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Decimal(\"0.10000\") + Decimal(\"0.20000\") == Decimal(\"0.3\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "Arithmetic operations between `Decimal` and `int` objects work as the latter are inherently precise: The results are *new* `Decimal` objects."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 165,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('42')"
+      ]
+     },
+     "execution_count": 165,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "21 + Decimal(21)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 166,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('42.0')"
+      ]
+     },
+     "execution_count": 166,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "10 * Decimal(\"4.2\")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 159,
+   "execution_count": 167,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4968,7 +5216,7 @@
        "Decimal('0.1')"
       ]
      },
-     "execution_count": 159,
+     "execution_count": 167,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4990,7 +5238,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 160,
+   "execution_count": 168,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5003,7 +5251,7 @@
        "'0.10000000000000000000000000000000000000000000000000'"
       ]
      },
-     "execution_count": 160,
+     "execution_count": 168,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5014,7 +5262,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 161,
+   "execution_count": 169,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5027,7 +5275,7 @@
        "'0.10000000000000000555111512312578270211815834045410'"
       ]
      },
-     "execution_count": 161,
+     "execution_count": 169,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5049,7 +5297,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 162,
+   "execution_count": 170,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5063,7 +5311,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-162-a3cea145e6d1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;36m1.0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m42\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-170-a3cea145e6d1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;36m1.0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m42\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for *: 'float' and 'decimal.Decimal'"
      ]
     }
@@ -5085,7 +5333,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 163,
+   "execution_count": 171,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5098,7 +5346,7 @@
        "Decimal('2')"
       ]
      },
-     "execution_count": 163,
+     "execution_count": 171,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5109,7 +5357,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 164,
+   "execution_count": 172,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5122,7 +5370,7 @@
        "Decimal('1.414213562373095048801688724')"
       ]
      },
-     "execution_count": 164,
+     "execution_count": 172,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5146,7 +5394,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 165,
+   "execution_count": 173,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5159,7 +5407,7 @@
        "Decimal('1.999999999999999999999999999')"
       ]
      },
-     "execution_count": 165,
+     "execution_count": 173,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5185,7 +5433,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 166,
+   "execution_count": 174,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5198,7 +5446,7 @@
        "Decimal('2.0000')"
       ]
      },
-     "execution_count": 166,
+     "execution_count": 174,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5220,7 +5468,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 167,
+   "execution_count": 175,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5234,7 +5482,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m                          Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-167-5b555b105c8f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtwo\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mquantize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"1e-28\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-175-5b555b105c8f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtwo\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mquantize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"1e-28\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m: [<class 'decimal.InvalidOperation'>]"
      ]
     }
@@ -5256,7 +5504,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 168,
+   "execution_count": 176,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5269,7 +5517,7 @@
        "True"
       ]
      },
-     "execution_count": 168,
+     "execution_count": 176,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5291,7 +5539,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 169,
+   "execution_count": 177,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5304,7 +5552,7 @@
        "True"
       ]
      },
-     "execution_count": 169,
+     "execution_count": 177,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5326,7 +5574,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 170,
+   "execution_count": 178,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5339,7 +5587,7 @@
        "Decimal('NaN')"
       ]
      },
-     "execution_count": 170,
+     "execution_count": 178,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5361,7 +5609,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 171,
+   "execution_count": 179,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5374,7 +5622,7 @@
        "False"
       ]
      },
-     "execution_count": 171,
+     "execution_count": 179,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5396,7 +5644,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 172,
+   "execution_count": 180,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5409,7 +5657,7 @@
        "Decimal('Infinity')"
       ]
      },
-     "execution_count": 172,
+     "execution_count": 180,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5420,7 +5668,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 173,
+   "execution_count": 181,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5433,7 +5681,7 @@
        "Decimal('-Infinity')"
       ]
      },
-     "execution_count": 173,
+     "execution_count": 181,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5444,7 +5692,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 174,
+   "execution_count": 182,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5457,7 +5705,7 @@
        "Decimal('Infinity')"
       ]
      },
-     "execution_count": 174,
+     "execution_count": 182,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5468,7 +5716,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 175,
+   "execution_count": 183,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5481,7 +5729,7 @@
        "True"
       ]
      },
-     "execution_count": 175,
+     "execution_count": 183,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5503,7 +5751,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 176,
+   "execution_count": 184,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5517,7 +5765,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m                          Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-176-87950ebbd6ef>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"-inf\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-184-87950ebbd6ef>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"-inf\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m: [<class 'decimal.InvalidOperation'>]"
      ]
     }
@@ -5528,7 +5776,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 177,
+   "execution_count": 185,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5542,7 +5790,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m                          Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-177-996083f200c6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-185-996083f200c6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m: [<class 'decimal.InvalidOperation'>]"
      ]
     }
@@ -5588,7 +5836,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 178,
+   "execution_count": 186,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5612,7 +5860,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 179,
+   "execution_count": 187,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5625,7 +5873,7 @@
        "Fraction(1, 3)"
       ]
      },
-     "execution_count": 179,
+     "execution_count": 187,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5636,7 +5884,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 180,
+   "execution_count": 188,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5649,7 +5897,7 @@
        "Fraction(1, 3)"
       ]
      },
-     "execution_count": 180,
+     "execution_count": 188,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5660,7 +5908,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 181,
+   "execution_count": 189,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5673,7 +5921,7 @@
        "Fraction(3333333333, 10000000000)"
       ]
      },
-     "execution_count": 181,
+     "execution_count": 189,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5684,7 +5932,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 182,
+   "execution_count": 190,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5697,7 +5945,7 @@
        "Fraction(3333333333, 10000000000)"
       ]
      },
-     "execution_count": 182,
+     "execution_count": 190,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5719,7 +5967,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 183,
+   "execution_count": 191,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5732,7 +5980,7 @@
        "Fraction(3, 2)"
       ]
      },
-     "execution_count": 183,
+     "execution_count": 191,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5743,7 +5991,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 184,
+   "execution_count": 192,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5756,7 +6004,7 @@
        "Fraction(3, 2)"
       ]
      },
-     "execution_count": 184,
+     "execution_count": 192,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5778,7 +6026,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 185,
+   "execution_count": 193,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5791,7 +6039,7 @@
        "Fraction(1, 10)"
       ]
      },
-     "execution_count": 185,
+     "execution_count": 193,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5813,7 +6061,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 186,
+   "execution_count": 194,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5826,7 +6074,7 @@
        "Fraction(3602879701896397, 36028797018963968)"
       ]
      },
-     "execution_count": 186,
+     "execution_count": 194,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5848,7 +6096,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 187,
+   "execution_count": 195,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5861,7 +6109,7 @@
        "Fraction(7, 4)"
       ]
      },
-     "execution_count": 187,
+     "execution_count": 195,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5872,7 +6120,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 188,
+   "execution_count": 196,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5885,7 +6133,7 @@
        "Fraction(1, 2)"
       ]
      },
-     "execution_count": 188,
+     "execution_count": 196,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5896,7 +6144,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 189,
+   "execution_count": 197,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5909,7 +6157,7 @@
        "Fraction(1, 1)"
       ]
      },
-     "execution_count": 189,
+     "execution_count": 197,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5920,7 +6168,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 190,
+   "execution_count": 198,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5933,7 +6181,7 @@
        "Fraction(1, 1)"
       ]
      },
-     "execution_count": 190,
+     "execution_count": 198,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5955,7 +6203,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 191,
+   "execution_count": 199,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5968,7 +6216,7 @@
        "0.1"
       ]
      },
-     "execution_count": 191,
+     "execution_count": 199,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5979,7 +6227,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 192,
+   "execution_count": 200,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5992,7 +6240,7 @@
        "'0.10000000000000000555111512312578270211815834045410'"
       ]
      },
-     "execution_count": 192,
+     "execution_count": 200,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6031,7 +6279,7 @@
     }
    },
    "source": [
-    "#### What is the solution to $x^2 = -1$ ?"
+    "**What is the solution to $x^2 = -1$ ?**"
    ]
   },
   {
@@ -6077,7 +6325,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 193,
+   "execution_count": 201,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6090,7 +6338,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 194,
+   "execution_count": 202,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6100,10 +6348,10 @@
     {
      "data": {
       "text/plain": [
-       "139674754426928"
+       "139663415663408"
       ]
      },
-     "execution_count": 194,
+     "execution_count": 202,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6114,7 +6362,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 195,
+   "execution_count": 203,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6127,7 +6375,7 @@
        "complex"
       ]
      },
-     "execution_count": 195,
+     "execution_count": 203,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6138,7 +6386,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 196,
+   "execution_count": 204,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6151,7 +6399,7 @@
        "1j"
       ]
      },
-     "execution_count": 196,
+     "execution_count": 204,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6173,7 +6421,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 197,
+   "execution_count": 205,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6186,7 +6434,7 @@
        "True"
       ]
      },
-     "execution_count": 197,
+     "execution_count": 205,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6208,7 +6456,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 198,
+   "execution_count": 206,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6221,7 +6469,7 @@
        "(2+0.5j)"
       ]
      },
-     "execution_count": 198,
+     "execution_count": 206,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6243,7 +6491,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 199,
+   "execution_count": 207,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6256,7 +6504,7 @@
        "(2+0.5j)"
       ]
      },
-     "execution_count": 199,
+     "execution_count": 207,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6278,7 +6526,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 200,
+   "execution_count": 208,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -6291,7 +6539,7 @@
        "(2+0j)"
       ]
      },
-     "execution_count": 200,
+     "execution_count": 208,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6313,7 +6561,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 201,
+   "execution_count": 209,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -6326,7 +6574,7 @@
        "(2+0.5j)"
       ]
      },
-     "execution_count": 201,
+     "execution_count": 209,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6337,7 +6585,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 202,
+   "execution_count": 210,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -6350,7 +6598,7 @@
        "(2+0.5j)"
       ]
      },
-     "execution_count": 202,
+     "execution_count": 210,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6372,7 +6620,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 203,
+   "execution_count": 211,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6386,7 +6634,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 204,
+   "execution_count": 212,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6399,7 +6647,7 @@
        "(4+6j)"
       ]
      },
-     "execution_count": 204,
+     "execution_count": 212,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6410,7 +6658,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 205,
+   "execution_count": 213,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6423,7 +6671,7 @@
        "(-2-2j)"
       ]
      },
-     "execution_count": 205,
+     "execution_count": 213,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6434,7 +6682,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 206,
+   "execution_count": 214,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -6447,7 +6695,7 @@
        "(2+2j)"
       ]
      },
-     "execution_count": 206,
+     "execution_count": 214,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6458,7 +6706,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 207,
+   "execution_count": 215,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -6471,7 +6719,7 @@
        "(0.5-4j)"
       ]
      },
-     "execution_count": 207,
+     "execution_count": 215,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6482,7 +6730,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 208,
+   "execution_count": 216,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -6495,7 +6743,7 @@
        "(5+10j)"
       ]
      },
-     "execution_count": 208,
+     "execution_count": 216,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6506,7 +6754,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 209,
+   "execution_count": 217,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -6519,7 +6767,7 @@
        "(0.5+0.6666666666666666j)"
       ]
      },
-     "execution_count": 209,
+     "execution_count": 217,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6530,7 +6778,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 210,
+   "execution_count": 218,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6543,7 +6791,7 @@
        "(-5+10j)"
       ]
      },
-     "execution_count": 210,
+     "execution_count": 218,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6554,7 +6802,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 211,
+   "execution_count": 219,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6567,7 +6815,7 @@
        "(0.44+0.08j)"
       ]
      },
-     "execution_count": 211,
+     "execution_count": 219,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6589,7 +6837,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 212,
+   "execution_count": 220,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6602,7 +6850,7 @@
        "5.0"
       ]
      },
-     "execution_count": 212,
+     "execution_count": 220,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6624,7 +6872,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 213,
+   "execution_count": 221,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6637,7 +6885,7 @@
        "1.0"
       ]
      },
-     "execution_count": 213,
+     "execution_count": 221,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6648,7 +6896,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 214,
+   "execution_count": 222,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6661,7 +6909,7 @@
        "2.0"
       ]
      },
-     "execution_count": 214,
+     "execution_count": 222,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6683,7 +6931,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 215,
+   "execution_count": 223,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6696,7 +6944,7 @@
        "(1-2j)"
       ]
      },
-     "execution_count": 215,
+     "execution_count": 223,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6784,7 +7032,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 216,
+   "execution_count": 224,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6797,7 +7045,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 217,
+   "execution_count": 225,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6825,7 +7073,7 @@
        " 'abstractmethod']"
       ]
      },
-     "execution_count": 217,
+     "execution_count": 225,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6851,7 +7099,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 218,
+   "execution_count": 226,
    "metadata": {
     "scrolled": true,
     "slideshow": {
@@ -6962,7 +7210,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 219,
+   "execution_count": 227,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -7142,7 +7390,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 220,
+   "execution_count": 228,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -7155,7 +7403,7 @@
        "1"
       ]
      },
-     "execution_count": 220,
+     "execution_count": 228,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7166,7 +7414,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 221,
+   "execution_count": 229,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7179,7 +7427,7 @@
        "42.87"
       ]
      },
-     "execution_count": 221,
+     "execution_count": 229,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7190,7 +7438,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 222,
+   "execution_count": 230,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7203,7 +7451,7 @@
        "5.0"
       ]
      },
-     "execution_count": 222,
+     "execution_count": 230,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7225,7 +7473,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 223,
+   "execution_count": 231,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -7238,7 +7486,7 @@
        "100"
       ]
      },
-     "execution_count": 223,
+     "execution_count": 231,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7249,7 +7497,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 224,
+   "execution_count": 232,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7262,7 +7510,7 @@
        "42"
       ]
      },
-     "execution_count": 224,
+     "execution_count": 232,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7284,7 +7532,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 225,
+   "execution_count": 233,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7298,7 +7546,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-225-e40cd01fb15a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mround\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2j\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-233-e40cd01fb15a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mround\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2j\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m: type complex doesn't define __round__ method"
      ]
     }
@@ -7333,7 +7581,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 226,
+   "execution_count": 234,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -7346,7 +7594,7 @@
        "True"
       ]
      },
-     "execution_count": 226,
+     "execution_count": 234,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7368,7 +7616,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 227,
+   "execution_count": 235,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7381,7 +7629,7 @@
        "True"
       ]
      },
-     "execution_count": 227,
+     "execution_count": 235,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7392,7 +7640,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 228,
+   "execution_count": 236,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7405,7 +7653,7 @@
        "True"
       ]
      },
-     "execution_count": 228,
+     "execution_count": 236,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7416,7 +7664,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 229,
+   "execution_count": 237,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7429,7 +7677,7 @@
        "True"
       ]
      },
-     "execution_count": 229,
+     "execution_count": 237,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7451,7 +7699,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 230,
+   "execution_count": 238,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7464,7 +7712,7 @@
        "False"
       ]
      },
-     "execution_count": 230,
+     "execution_count": 238,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7486,7 +7734,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 231,
+   "execution_count": 239,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -7499,7 +7747,7 @@
        "True"
       ]
      },
-     "execution_count": 231,
+     "execution_count": 239,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7534,7 +7782,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 232,
+   "execution_count": 240,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -7585,7 +7833,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 233,
+   "execution_count": 241,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -7598,7 +7846,7 @@
        "1"
       ]
      },
-     "execution_count": 233,
+     "execution_count": 241,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7609,7 +7857,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 234,
+   "execution_count": 242,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7622,7 +7870,7 @@
        "6"
       ]
      },
-     "execution_count": 234,
+     "execution_count": 242,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7633,7 +7881,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 235,
+   "execution_count": 243,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7646,7 +7894,7 @@
        "6"
       ]
      },
-     "execution_count": 235,
+     "execution_count": 243,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7668,7 +7916,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 236,
+   "execution_count": 244,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -7682,8 +7930,8 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-236-188b816be8b6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-232-0b8c729be194>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n, strict)\u001b[0m\n\u001b[1;32m     17\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mReal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mstrict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 19\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"n is not integer-like; it has decimals\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     20\u001b[0m             \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-244-188b816be8b6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-240-0b8c729be194>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n, strict)\u001b[0m\n\u001b[1;32m     17\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mReal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mstrict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 19\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"n is not integer-like; it has decimals\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     20\u001b[0m             \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mTypeError\u001b[0m: n is not integer-like; it has decimals"
      ]
     }
@@ -7705,7 +7953,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 237,
+   "execution_count": 245,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -7718,7 +7966,7 @@
        "6"
       ]
      },
-     "execution_count": 237,
+     "execution_count": 245,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7740,7 +7988,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 238,
+   "execution_count": 246,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -7754,8 +8002,8 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-238-7296a74f5dcf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2j\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-232-0b8c729be194>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n, strict)\u001b[0m\n\u001b[1;32m     20\u001b[0m             \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is only defined for integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-246-7296a74f5dcf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2j\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-240-0b8c729be194>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n, strict)\u001b[0m\n\u001b[1;32m     20\u001b[0m             \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is only defined for integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mTypeError\u001b[0m: Factorial is only defined for integers"
      ]
     }
@@ -7824,7 +8072,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 239,
+   "execution_count": 247,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -7846,10 +8094,10 @@
        "        "
       ],
       "text/plain": [
-       "<IPython.lib.display.YouTubeVideo at 0x7f089024e2d0>"
+       "<IPython.lib.display.YouTubeVideo at 0x7f05ec430a10>"
       ]
      },
-     "execution_count": 239,
+     "execution_count": 247,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7861,7 +8109,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 240,
+   "execution_count": 248,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -7883,10 +8131,10 @@
        "        "
       ],
       "text/plain": [
-       "<IPython.lib.display.YouTubeVideo at 0x7f08901d2650>"
+       "<IPython.lib.display.YouTubeVideo at 0x7f05ec42ac90>"
       ]
      },
-     "execution_count": 240,
+     "execution_count": 248,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7908,7 +8156,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 241,
+   "execution_count": 249,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -7930,10 +8178,10 @@
        "        "
       ],
       "text/plain": [
-       "<IPython.lib.display.YouTubeVideo at 0x7f08901dad50>"
+       "<IPython.lib.display.YouTubeVideo at 0x7f05ec428650>"
       ]
      },
-     "execution_count": 241,
+     "execution_count": 249,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -7942,6 +8190,53 @@
     "YouTubeVideo(\"4qH4unVtJkE\", width=\"60%\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "This video by the YouTube channel [Computerphile](https://www.youtube.com/channel/UC9-y-6csu5WGm29I7JiwpnA) explains floating point numbers in an intuitive way with some numeric examples."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 250,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/jpeg": 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\n",
+      "text/html": [
+       "\n",
+       "        <iframe\n",
+       "            width=\"60%\"\n",
+       "            height=\"300\"\n",
+       "            src=\"https://www.youtube.com/embed/PZRI1IfStY0\"\n",
+       "            frameborder=\"0\"\n",
+       "            allowfullscreen\n",
+       "        ></iframe>\n",
+       "        "
+      ],
+      "text/plain": [
+       "<IPython.lib.display.YouTubeVideo at 0x7f05ec426110>"
+      ]
+     },
+     "execution_count": 250,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "YouTubeVideo(\"PZRI1IfStY0\", width=\"60%\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -7955,7 +8250,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 242,
+   "execution_count": 251,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -7977,10 +8272,10 @@
        "        "
       ],
       "text/plain": [
-       "<IPython.lib.display.YouTubeVideo at 0x7f08901e47d0>"
+       "<IPython.lib.display.YouTubeVideo at 0x7f05ec411c10>"
       ]
      },
-     "execution_count": 242,
+     "execution_count": 251,
      "metadata": {},
      "output_type": "execute_result"
     }