Georg Cantor and the Idea of Infinity

Educators are always talking about "what mathematicians really do." Fact is, they do lots of very different things, most of which require technical vocabulary and a lot of mathematical background

Around 1890, Georg Cantor invents a theory of infinite sets and shocks the mathematical world. Luckily, this theory is not only genuinely elegant, but doesn't require much background. So, it's a wonderful example for both high school teachers and students to show at least what some mathematicians do or have done.

Prior to the talk, please think about the following excerpt from a Jonathan Swift poem: 

A flea

Has smaller fleas that on him prey

And these have smaller still to bite 'em,  

And so proceed ad infinitum.