Set Theory — History & Overview

Part I — What Is Set Theory & Why Is It Relevant Today?

Originally Published: https://www.setzeus.com/

The concept of infinity is ideologically far from the average math terminology — no other topic transverses outside the circle of math in a way that’s translated from a practical, analytical tool to a phenomena of mythical renown. Rubbing shoulders with cultural topics such as religion & philosophy, the notion of infinity holds a peculiar aura of divinity.

Once upon a time it was a foundational given, in all academic disciplines, that there existed a single infinity.

Then, in 1874, a relatively obscure mathematician unleashed a consortium of ground-breaking observations & revolutionary questions targeting this worldly, deeply-held belief. One Georg Cantor, in his now legendary publication On a Property of the Collection of All Real Algebraic Numbers proved that the set of real numbers is “more numerous” than the set of real, algebraic numbers. This showed, for the first time, that there exists infinite sets of different sizes (don’t-worry — we’ll review his paper in detail shortly for clarification).

A Set Is Many That Allows Itself To Be Though Of As One — Georg Cantor