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

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Wizard-Of-Oz

Posts: 404
Registered: 12/28/13
Re: The self-contradictory infinite hotel
Posted: Feb 23, 2014 8:30 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

John Gabriel <thenewcalculus@gmail.com> wrote in
news:f28dcac1-ab44-4ffa-94be-9927e5a3586f@googlegroups.com:

> On Sunday, 23 February 2014 12:50:47 UTC+2, Wizard-Of-Oz wrote:
>

>> Surely saying all rooms are occupied
>> is equivalent to Saying there is no room that is unoccupied
>> In either case, there would be no need for a 'last room'.

>
> This is what he said:


He who?

> But, if there is no last room, it can never be the case that *all*
> rooms are occupied,


It depends on whether there are enough guests for each room.

If there is a one-to-one mapping of guests to rooms, then it IS the case
that all the rooms are occupied.

If not, then one would be able to nominate which room is NOT occupied.

> hence the whole argument, for how informal, falls
> apart since inception.
>
> No last room => all rooms not occupied.


No .. it doesn't imply that at all.

Why would all of the room be unoccupied? Or did you mean to say 'not
all rooms occupied'? In which case it depends on the set of guests.

If there is a finite number of guests, then no last room means that some
rooms are unoccupied, because there is no one-to-one mapping from the
set of guests to the set of rooms, and the set of rooms is always larger
than any finite set of guests.

If there is no unoccupied room (the hotel is 'full') then there IS a
one-to-one mapping of guests to rooms. Both sets are 'infinite'.

> What you are saying is:
>
> All rooms occupied => no last room.


I didn't say that at all. If you're going to criticise, as least
criticise what I said, and not your own inventions of what you imagine I
said.

I said that neither statement ("all rooms are occupied", or "no room is
unoccupied") requires there to be a last room. It ONLY requires that if
we ALSO say that there is a finite number of guwests.

> That would result in
>
> All rooms occupied => no last room => all rooms not occupied


If either of the implication were true, then it would. But it doesn't

> Do you notice something wrong with that O moron? Clue: contradiction.

Clue: you're a moron

> Surely you missed that? :-)

You simply can't read. That's not my problem, its yours.


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

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