LudovicoVan
Posts:
4,165
From:
London
Registered:
2/8/08
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The self-contradictory infinite hotel (2)
Posted:
Feb 24, 2014 6:40 PM
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"Consider a hypothetical hotel with a countably infinite number of rooms,
all of which are occupied." (*)
To say that the hotel is fully occupied is to say that, for all n in N, room
n is occupied. Therefore, room 1 is occupied and, for all n in N, if room n
is occupied, room n+1 is also occupied. Hence, for all n in N, it is not
the case that a guest can move from room n to room n+1. Namely, no more
guests can be accommodated. QED.
Julio
(*) http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel
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