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That's sort of the entire point of the paradox. Every room is full at the start. Not "somehow at least one is not", but every single room is full. Then, by h
by MereInterest 5y ago
That's sort of the entire point of the paradox. Every room is full at the start. Not "somehow at least one is not", but every single room is full. Then, by having guests move to different rooms, you can rearrange such that there is an empty room.
The guests are markers to indicate a bijective function between room numbers. Each guest represents a (before, after) tuple.
- rightbyte 5y agoA point of a paradox can also be to invalidate the assumptions made. I mean, mathematicians are getting away with way too much nonsense by using diffucult words. The hotel paradox is essentially equivalent to: I can add a natural number to the set of all natural numbers which is not in the set allready.
- morelisp 5y agoNo, the paradox is that there are the same number of even natural numbers and natural numbers, yet the former is a strict subset of the latter.
- rightbyte 5y agoYe sorry I was refering to the hotel paradox. Edited.
- MereInterest 5y agoI think I would call that a contradiction rather than a paradox. A conclusion that is a contradiction means that one of your starting assumptions is incorrect. A conclusion that is a paradox means that your intuition about the problem was incorrect.