Outdoing Infinity
Is it possible to outdo this? Can you beat infinity? Can your score be higher than toldorknown’s? Yes, it can.
One of the most beautiful pieces of logic (that can be understood by most people) I know of is Cantor’s Diagonal Proof of the uncountability of the real numbers. My first paragraph here was a shameless attempt to get you to read on long enough for me to explain, without scaring you all away with a stack of technical adjectives.
The diagonal proof shows that there is something larger than infinity. It shows that one infinity can be larger than another. It’s quite wonderful. The proof shows this by showing that the set of all integer is, in a meaningful sense, larger than the set of reals. There’s an infinity of integers (-1, 42, 0, 129, -8402975, etc.), but there are even more real numbers. One infinity > another.
I’m confused, but never mind.
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