Cantor’s Diagonal Argument: Why Some Infinities Are Bigger Than Others

When Cantor’s Diagonal Argument Shows Up Twice in Three Days

Funny how things line up sometimes. Over the past three days, I’ve come across Cantor’s diagonal argument twice — in two separate popular videos with audiences in the millions. First in this video by Topless about Hilbert’s Hotel and infinity, and then in yesterday’s episode by Veritasium — also about infinity and Cantor himself.

On one hand, these topics feel almost worn out. You’d think there are already dozens of great videos on the subject.

How Many Good Videos on the Cantor Diagonal Argument Actually Exist?

On the other hand — not really. There are maybe two or three genuinely good episodes on infinity (here, here, and here). A few more solid books.

But there’s a third angle — and it’s the most important one. Beautiful mathematics can never be overdone. Fascinating ideas that genuinely make your brain stir can be revisited again and again, from different angles, uncovering new meaning or reframing familiar ones. Veritasium itself previously made a video about Hilbert’s Hotel where the diagonal element also appeared.

Infinity and the Cantor Diagonal Argument — A Topic Worth Returning To

When the time comes, we’ll dig into infinity too — once we’ve gone a little deeper. For now, it’s time to start preparing an episode on something more practical, but equally deceptive and confusing.

What about you? What would you like to learn about infinity?