How many sizes of infinity are there?

“O God, I could be bound in a nutshell, and count myself a king of infinite space – were it not that I have bad dreams.”

Hamlet, Act 2, Scene 2. Lines 252-254.

Recently, a colleague asked me:

I know that there are different sizes of infinity, but what I want to know is how many different sizes of infinity there are?

-Curious Colleague

This is a great question! I tried to explain my answer at the time, but it came out garbled and I think I confused him more than I helped. So this post is an effort to remedy that and answer his question.

Continue reading How many sizes of infinity are there?