A Saga on Infinity: Cantor and the Theory of Sets

In the Three Body Problem, there's this genius mathematician, Wei Cheng. When other scientists struggled to find specific stable solutions (they only managed to find 2-3, if my memory serves), Wei had found hundreds.

Cantor is the real life Wei. His work on set theory had been so revolutionary that, at the time, it was widely rejected, and Cantor himself was admitted to a mental hospital. In this article, we will review the key points of Cantor's Theory of Sets, and hopefully at the end you will develop a deep appreciation to this cornerstone that underpins much of contemporary mathematics.

First let's be clear, Cantor did not invent the concepts of 'sets.' His work stands out specifically on infinite sets. For example, he divided infinite sets into:

• Countable Infinite Sets: There is a one-to-one correspondence between its elements and the natural numbers ().
• Uncountable Infinite Sets: There isn't one-to-one correspondence between its elements and the natural numbers.