Long read · Mind-bend
Cantor's Infinity
There are bigger infinities than infinity. In 1874 a young German mathematician proved it. The reaction was so hostile his career nearly didn't survive. Here is the proof, in plain English, and the story of the man who paid for it.
Quick answer
Yes, there are infinities bigger than other infinities. The infinity of whole numbers (1, 2, 3...) is the smallest one. The infinity of real numbers is strictly bigger. Georg Cantor proved this in 1874 with a single beautiful argument called the diagonal proof. It shows that no matter how you try to list every real number, you can always construct a real number that isn't in your list. Therefore the reals cannot be listed; therefore there are more of them than there are positions in any list, even an infinite one.
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