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Table of Contents

1. 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*}

This definition of infinity is generally used to define concepts such as in mathematics.

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