Re: The reality of sets, on a scale of 1 to 10

Am Wed, 02 Apr 2025 15:58:05 +0200 schrieb WM:

On 27.03.2025 22:31, joes wrote:

Am Thu, 27 Mar 2025 20:31:16 +0100 schrieb WM:

Am 27.03.2025 um 15:59 schrieb joes:

Am Wed, 26 Mar 2025 21:28:52 +0100 schrieb WM:

On 26.03.2025 21:06, joes wrote:

Am Wed, 26 Mar 2025 20:36:40 +0100 schrieb WM:

>

The potential infinite is a variable finite. Cantor's actual
infinity is not variable but fixed. (Therefore Hilbert's hotel is
potential infinity.)

What we refer to as infinite isn't variable.

The number of guests/rooms in Hilbert's hotel is infinite but can
grow. That is variable infinity.

The number of rooms is fixed,

One more guest requires one more room.

*Which is already there*. We are not building new rooms, we are moving
the guests.

That is only possible if it is possible, i.e., ifinfinity is potential
never occupied completely. That contradicts the completeness of Cantor's
bijections.

I can't guess what you edited this from. Can you write it again?
Anyway, infinity is infinite, no need to hide anything in "potential
darkness". This is just your crutch to understand it as finite.

otherwise it weren't interesting.

It is interesting only insofar as it shows that adherents of set
theory are ready to believe every shit.

Do you believe Hilbert's Hotel cannot accomodate *any* new guests?

If it is actually infinite, then no. If it can accomodate every new
guest, then it is never completely filled.

You would be mistaken. There are never empty rooms, all rooms are
always occupied, that's kinda the point. And yet it can accommodate
a countable number of guests, unlike if it were finite.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.