Re: Contradiction in mathematics Hilbert's paradox of the Grand Hotel

byron says...

quote

"Then imagine a hotel, called Grand Hotel, with an* infinite number of
rooms, which is *full*, so there's a guest in each room. Unlike normal
hotels, we still can find a room for a new guest: we move the guest in
room number 1 into the room number 2, then the one in the room number
2 into number 3, and we keep moving guests until every guest who was,
at start, in room number n, is moved to room number n+1, and finally
we move the new guest into the room number one. This shows how we can
find a room for a new guest even if the hotel is already full,
something that could not happen in any hotel with a finite number of
rooms."

That's what I said. An infinite hotel can always take in one more
guest.

an infinity cant be finite ie full
by the fact that hilbert has an infinity being full
indicates there cant not be an infinity in the first place
hilbert in fact talks in contradictory terms
thus
generating his paradox- which hinges on his infinity being
contradictory full

There is no contradiction. Let's spell out the Hilbert Hotel
in more detail.

There is a set R of rooms. There is a time-dependent set G(t)
of guests. There is a time-dependent assignment assign(t,g) which
tells which room is assigned to guest g at time t.

To say the hotel is "full" at time t is to say that for every room r,
there is a guest g such that assign(t,g) = r. In other words, every
room is assigned to some guest.

For an finite hotel, if the hotel is full at time t, then it will
still be full at time t+1, unless some guests check out. For an
infinite hotel, that's not the case. You can make a full hotel
become not full by changing the room assignments.

--
Daryl McCullough
Ithaca, NY

.

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