John Gabriel <firstname.lastname@example.org> wrote in news:email@example.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:
> 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.