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Diffstat (limited to 'mindmap/infinity.org')
| -rw-r--r-- | mindmap/infinity.org | 18 |
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diff --git a/mindmap/infinity.org b/mindmap/infinity.org index b08e723..8d41105 100644 --- a/mindmap/infinity.org +++ b/mindmap/infinity.org @@ -3,7 +3,19 @@ :END: #+title: infinity #+author: Preston Pan -#+options: num:nil #+html_head: <link rel="stylesheet" type="text/css" href="../style.css" /> -#+options: tex:dvipng -* placeholder text +#+html_head: <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> +#+html_head: <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> +#+options: broken-links:t + +* Introduction +Infinity has been a concept that has caused many troubles in the realm of mathematics. Algebra with infinities +have not been easy to define in history, and there are limited cases of success in this endevour. Generally speaking, +we can add infinities to existing sets, and define ordering. For example, for real numbers, the set: +\begin{align*} +\mathbb{R}\cup \{-\infty, \infty \} +\end{align*} +extends the real numbers to include infinites. However, only order is well defined; algebra is generally not allowed. +\begin{align*} +\forall a \in \mathbb{R}, -\infty < a < \infty +\end{align*} |