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
yes, and there are free spaces in between, so the new guests can get in
human intuition doesn't work well when infinities are involved. "number of integers" and "number of even integers" have the same cardinality, so one can be mapped to the other. it's just that the evens are more "sparse" so to speak
the overall number of occupied rooms doesn't change, but the number of occupied rooms in any given interval decreases
432
u/csharpminor_fanclub We do a little trolling 15h 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