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Alexander Hess 2024-04-08 22:13:31 +02:00
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8
05_numbers/02_content.ipynb
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@ -8,7 +8,7 @@
}
},
"source": [
"**Note**: Click on \"*Kernel*\" > \"*Restart Kernel and Clear All Outputs*\" in [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/) *before* reading this notebook to reset its output. If you cannot run this file on your machine, you may want to open it [in the cloud <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_mb.png\">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/05_numbers/02_content.ipynb)."
"**Note**: Click on \"*Kernel*\" > \"*Restart Kernel and Clear All Outputs*\" in [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/) *before* reading this notebook to reset its output. If you cannot run this file on your machine, you may want to open it [in the cloud <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_mb.png\">](https://mybinder.org/v2/gh/webartifex/intro-to-python/main?urlpath=lab/tree/05_numbers/02_content.ipynb)."
]
},
{
@ -697,7 +697,7 @@
}
},
"source": [
"Analogous to the discussion of *containers* and *iterables* in [Chapter 4 <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/04_iteration/02_content.ipynb#Containers-vs.-Iterables), we contrast the *concrete* numeric data types in this chapter with the *abstract* ideas behind [numbers in mathematics <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Number).\n",
"Analogous to the discussion of *containers* and *iterables* in [Chapter 4 <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/main/04_iteration/02_content.ipynb#Containers-vs.-Iterables), we contrast the *concrete* numeric data types in this chapter with the *abstract* ideas behind [numbers in mathematics <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Number).\n",
"\n",
"The figure below summarizes five *major* sets of [numbers in mathematics <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Number) as we know them from high school:\n",
"\n",
@ -819,7 +819,7 @@
"\n",
"For, example, as all numeric data types are `Complex` numbers in the abstract sense, they all work with the built-in [abs() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#abs) function (cf., [documentation <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/numbers.html#numbers.Complex)). While it is intuitively clear what the [absolute value <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Absolute_value) (i.e., \"distance\" from $0$) of an integer, a fraction, or any real number is, [abs() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#abs) calculates the equivalent of that for complex numbers. That concept is called the [magnitude <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Magnitude_%28mathematics%29) of a number, and is really a *generalization* of the absolute value.\n",
"\n",
"Relating back to the concept of **duck typing** mentioned in [Chapter 4 <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/04_iteration/00_content.ipynb#Duck-Typing), `int`, `float`, and `complex` objects \"walk\" and \"quack\" alike in context of the [abs() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#abs) function."
"Relating back to the concept of **duck typing** mentioned in [Chapter 4 <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/main/04_iteration/00_content.ipynb#Duck-Typing), `int`, `float`, and `complex` objects \"walk\" and \"quack\" alike in context of the [abs() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#abs) function."
]
},
{
@ -1174,7 +1174,7 @@
}
},
"source": [
"However, if we model `1 / 10` as a `Fraction` object (cf., [Appendix <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/05_numbers/03_appendix.ipynb#The-Fraction-Type)), it is recognized as a `Rational` number."
"However, if we model `1 / 10` as a `Fraction` object (cf., [Appendix <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/main/05_numbers/03_appendix.ipynb#The-Fraction-Type)), it is recognized as a `Rational` number."
]
},
{