Thread: Hilbert Hotel

Originally Posted by David E. Eaton Sr.

Originally Posted by Coelacanth

As I understand grapes's position, the set of counting numbers is infinite, but the elements in the set are finite.

[COLOR="purple"][I]Agreed... And I think we've all agreed on these two points.

The "labels", in order, are just the counting numbers too!

So, as I've said, each one is finite, but there is an unlimited number of them (that is, infinite). What I've said all along.

It looks like the three of us agree?

Originally Posted by grapes

The "labels", in order, are just the counting numbers too!

So, as I've said, each one is finite, but there is an unlimited number of them (that is, infinite). What I've said all along.

It looks like the three of us agree?

So, what is the next topic...

It's Ray's (sub) topic, I'll wait for him.

Oh, I bowed out as it was all going so well without me. :-)

There is much more to Hilbert's Hotel, but I have forgotten it.
More here: Hilbert's paradox of the Grand Hotel - Wikipedia, the free encyclopedia

Are you our fourth then?

Originally Posted by grapes

Are you our fourth then?

We have a fourth??? Who has the cards??

Was just reading Morris Kline's The Loss of Certainty, and he claims that Poincaré said that infinity is just our concept of being able to make an unlimited quantity of whatever, that Poincaré didn't believe in an actual infinity. I'll get the exact quote when I have the book with me.

From the Poincaré wiki:

He never spent a long time on a problem since he believed that the subconscious would continue working on the problem while he consciously worked on another problem.
In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré started from basic principles each time (O'Connor et al., 2002).

Poincare was a sharp cookie. Mandelbrot was clever, but much of his work was preceded by Poincare decades before.

Poincaré might've got more credit for relativity if he'd believed in it.

And, if he hadn't died so early.