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Topic: The self-contradictory infinite hotel (2)
Replies: 35   Last Post: Mar 2, 2014 6:16 PM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
The self-contradictory infinite hotel (2)
Posted: Feb 24, 2014 6:40 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"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




Date Subject Author
2/24/14
Read The self-contradictory infinite hotel (2)
LudovicoVan
2/24/14
Read Re: The self-contradictory infinite hotel (2)
Peter Percival
2/24/14
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LudovicoVan
2/24/14
Read Re: The self-contradictory infinite hotel (2)
Virgil
2/25/14
Read Re: The self-contradictory infinite hotel (2)
Richard Tobin
2/25/14
Read Re: The self-contradictory infinite hotel (2)
LudovicoVan
2/26/14
Read Re: The self-contradictory infinite hotel (2)
Wizard-Of-Oz
2/25/14
Read Re: The self-contradictory infinite hotel (2)
ross.finlayson@gmail.com
2/26/14
Read Re: The self-contradictory infinite hotel (2)
Virgil
2/26/14
Read Re: The self-contradictory infinite hotel (2)
ross.finlayson@gmail.com
2/26/14
Read Re: The self-contradictory infinite hotel (2)
thenewcalculus@gmail.com
2/27/14
Read Re: The self-contradictory infinite hotel (2)
ross.finlayson@gmail.com
2/28/14
Read Re: The self-contradictory infinite hotel (2)
Phil Carmody
2/28/14
Read Re: The self-contradictory infinite hotel (2)
LudovicoVan
2/28/14
Read Re: The self-contradictory infinite hotel (2)
Tucsondrew@me.com
2/28/14
Read Re: The self-contradictory infinite hotel (2)
Wizard-Of-Oz
2/28/14
Read Re: The self-contradictory infinite hotel (2)
Tucsondrew@me.com
3/1/14
Read Re: The self-contradictory infinite hotel (2)
Wizard-Of-Oz
3/2/14
Read Re: The self-contradictory infinite hotel (2)
LudovicoVan
3/2/14
Read Re: The self-contradictory infinite hotel (2)
thenewcalculus@gmail.com
3/2/14
Read Re: The self-contradictory infinite hotel (2)
LudovicoVan
3/2/14
Read Re: The self-contradictory infinite hotel (2)
thenewcalculus@gmail.com
3/2/14
Read Re: The self-contradictory infinite hotel (2)
Wizard-Of-Oz
3/2/14
Read Re: The self-contradictory infinite hotel (2)
Wizard-Of-Oz
3/2/14
Read Re: The self-contradictory infinite hotel (2)
Wizard-Of-Oz
3/2/14
Read Re: The self-contradictory infinite hotel (2)
LudovicoVan
3/2/14
Read Re: The self-contradictory infinite hotel (2)
Wizard-Of-Oz
3/2/14
Read Re: The self-contradictory infinite hotel (2)
Tucsondrew@me.com
3/2/14
Read Re: The self-contradictory infinite hotel (2)
John Gabriel
3/2/14
Read Re: The self-contradictory infinite hotel (2)
Wizard-Of-Oz
2/28/14
Read Re: The self-contradictory infinite hotel (2)
Phil Carmody
2/24/14
Read Re: The self-contradictory infinite hotel (2)
Virgil
2/24/14
Read Re: The self-contradictory infinite hotel (2)
LudovicoVan
2/24/14
Read Re: The self-contradictory infinite hotel (2)
Virgil
2/26/14
Read Re: The self-contradictory infinite hotel (2)
thenewcalculus@gmail.com
2/26/14
Read Re: The self-contradictory infinite hotel (2)
thenewcalculus@gmail.com

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