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

Am Thu, 27 Mar 2025 21:15:39 +0100 schrieb WM:

Am 26.03.2025 um 22:38 schrieb Alan Mackenzie:

WM <wolfgang.mueckenheim@tha.de> wrote:

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.

You are mistaken.  (Countable) infinity stays the same when you add
finite and countably infinite numbers to it.

That proves that cardinality is nonsense. When a new guest arrives, then
the number of guests grows by 1.

It's just counterintuitive, which is excusable, as opposed to your
wilfull ignorance. Yes, but the new number is also still equal, it
does not become "more infinite"/uncountable.

Thus in Hilbert's hotel,
although all the rooms are occupied, one of these rooms can be vacated
to make room for a new guest without expelling an existing guest.

Real fools are really delighted by counterintuitive results.

Natural fools hold their intuition above all.

Adding that new guest doesn't change the number of guests in the hotel,
or the number of rooms required.

Real fools are really delighted by counterintuitive results.

That's what makes math fun.

 See many of Jim's posts over the last few days for details.

There is only one important detail, namely that lossless exchanges cause
losses. It is sufficient to reject every intelligent being.

That's a misrepresentation.

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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.