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Topic: The self-contradictory infinite hotel
Replies: 62   Last Post: Feb 24, 2014 10:17 PM

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LudovicoVan

Posts: 3,206
From: London
Registered: 2/8/08
The self-contradictory infinite hotel
Posted: Feb 22, 2014 10:11 PM
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"Consider a hypothetical hotel with a countably infinite number of rooms,
all of which are occupied." (*)

The nature of countable infinity is such that there cannot be a last room,
and that's fundamental to the fact that new guests can be accommodated in an
infinite hotel at will, itself an illustration of the fact that we can count
endlessly. But, if there is no last room, it can never be the case that
*all* rooms are occupied, hence the whole argument, for how informal, falls
apart since inception.

More logical seems to say that, while there can be ideal constructs such as
the actual infinities of super-tasks and corresponding "super-numbers",
there can be no such thing as the standard countable infinity, as that would
be something that at the same time is and is not exhausted, i.e. a
self-contradictory notion. Finite infinity is rather just that, the ever
unfinished.

Julio

(*) http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel




Date Subject Author
2/22/14
Read The self-contradictory infinite hotel
LudovicoVan
2/22/14
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thenewcalculus@gmail.com
2/23/14
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Virgil
2/23/14
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2/23/14
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LudovicoVan
2/23/14
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LudovicoVan
2/23/14
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2/23/14
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LudovicoVan
2/23/14
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Virgil
2/23/14
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fom
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2/24/14
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LudovicoVan
2/24/14
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2/24/14
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LudovicoVan
2/23/14
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2/24/14
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2/24/14
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2/23/14
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2/23/14
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2/23/14
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YBM
2/23/14
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John
2/23/14
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LudovicoVan
2/23/14
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fom
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LudovicoVan
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Virgil
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fom
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Virgil
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2/24/14
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LudovicoVan
2/23/14
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William Elliot
2/23/14
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Richard Tobin
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Wizard-Of-Oz
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2/23/14
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2/23/14
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thenewcalculus@gmail.com
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2/23/14
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David C. Ullrich
2/23/14
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2/24/14
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2/24/14
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byron
2/24/14
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Peter Percival
2/24/14
Read Re: The self-contradictory infinite hotel
Virgil

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