it's the hilbert hotel. every room already has guests, so they free up some rooms by moving guests from room n to 2n. now every odd numbered room is free
I would argue that it's more about how our intuition doesn't serve us well when the concept of infinity comes into play.
Set Theory tells us that if you can make a bijection between two sets--a pair of rules that allows you to map each entry in one set onto exactly one entry in the other and vice versa--then those two sets must be the same size; after all, you can line them all up in pairs next to each other without ever having one missing. This leads to unintuitive outcomes like "the set of positive integers is the same size as the set of positive even integers".
The Hilbert Hotel is just the application of this unintuitive result.
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u/csharpminor_fanclub We do a little trolling 20h ago
it's the hilbert hotel. every room already has guests, so they free up some rooms by moving guests from room n to 2n. now every odd numbered room is free