Some infinities are bigger than other infinities. Here's how we know that.

Minute Physics' Henry Reich takes a break from physics to drop some maths knowledge. Using some basic tenets of set theory, Reich explains how we know that one infinity can be bigger than another.

It might take you a couple of run-throughs, but the concepts he's presenting here are actually pretty straight forward, which is kind of funny for a couple of reasons. For one thing, while demonstrating the existence of infinite infinites may be relatively painless, actually sitting by yourself and thinking about the existence of infinite infinities is still an excellent way to trigger a nose bleed and make your eyes roll back.

And two, for as "simple" as the idea of infinite infinities comes across in a 120-second YouTube video, nobody had actually demonstrated this concept (let alone that some infinites were bigger than others) until the late 1800s. Thanks for the brain cramps, Georg Cantor!


For a more in-depth look at infinity and all its weirdness, check out our brief (but thorough) introduction.

Share This Story

Get our newsletter


I don't get it. It seems the crux of this argument is that you can somehow always write a new number between 0 and 1 (he uses 0.52783... as the example) that will be "different from all the other numbers we've drawn lines to, but we've already drawn a line from every integer."

And that's where he loses me. How have we already drawn a line through every integer? It seems to me you can go in the opposite direction and this will also still hold true. That is, you can always write a new integer (just add 1) the same way you can always write a new number between 0 and 1 and then say "but we've already drawn a line from every number between 0 and 1."

Apparently my brain is not large enough to contain infinity. Let alone different infinities.