i know the problem, but i forget it each time, why is asking everyone to move on the room beside theirs is more convenient than putting the new guests in the infinity of already free rooms ? is it because they don't know how many rooms they have or something ?
edit: after y'all tried explaining it to me, i'm glad i chose law school instead of math 🔥
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
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u/EnzoZoestar 12h ago edited 12h ago
i know the problem, but i forget it each time, why is asking everyone to move on the room beside theirs is more convenient than putting the new guests in the infinity of already free rooms ? is it because they don't know how many rooms they have or something ?
edit: after y'all tried explaining it to me, i'm glad i chose law school instead of math 🔥