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From: WM <invalid@no.org>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The
 non-existence of "dark numbers"]
Date: Thu, 27 Mar 2025 21:15:39 +0100
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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.

> 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.
> 
> 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.

>  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.

REgards, WM