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From: Alan Mackenzie <acm@muc.de>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]
Date: Fri, 28 Mar 2025 15:45:47 -0000 (UTC)
Organization: muc.de e.V.
Message-ID: <vs6g7b$2mp5$1@news.muc.de>
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WM <invalid@no.org> wrote:
> 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.

Yes indeed.  There were aleph-0 guests beforehand, the new guest arrives
growing that number by 1, giving aleph-0.  Why do you find this so
difficult to understand?

>> 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.

You've run out of mathematics, so you resort to ad hominem.  Not very
good.  Hint: the person who devised "Hilbert's hotel" was in no sense a
fool.

>> 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.

An infinite process of lossless exchanges can cause loss, as we have
seen.

> Regards, WM

-- 
Alan Mackenzie (Nuremberg, Germany).