[ducttapecrown]

This speaks of the mathematical notion of cardinality, which is the number of elements in a set. For infinite sets, it turns out there are multiple sizes. The natural numbers have the smallest infinite size, and it is the same size of set as the integers and perhaps surprisingly, the rationals. But the real numbers have more elements. A quick proof is called Cantor's diagonalization argument, I recommend looking it up!

In fact, I recently learned there is one cardinality for each possible way to order an infinite set. This is slightly confusing because there are many ordinals of each cardinality, but there are just that many cardinals I've decided.

[rvbissell]

I missed your suggestion about Cantor's diagonalization earlier today, but I thank you for bringing it to my attention. That is quite clever.