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From: Alan Mackenzie <acm@muc.de>
Newsgroups: sci.math
Subject: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]
Date: Fri, 21 Mar 2025 18:48:40 -0000 (UTC)
Organization: muc.de e.V.
Message-ID: <vrkca8$18dh$1@news.muc.de>
References: <vqrbtd$1chb7$2@solani.org>   <ae5edd89-d5da-4ff4-a723-485cafa92582@att.net> <vrc8n0$2og7i$2@dont-email.me> <0b8644b2-7027-420e-b187-8214daaf9e3b@att.net> <vrf5bp$1gcun$1@dont-email.me> <b3730bf7-bcd1-4698-b465-6d6ef190b29d@att.net> <vrgm1k$2s8c6$2@dont-email.me> <c81100d7-9354-4c8e-b216-e147cab9b41c@att.net> <vrhrlb$3ta8t$1@dont-email.me> <c0de7504-7d17-42f1-83e8-8767c0859c0c@att.net> <vrj5nh$12273$1@dont-email.me> <efbe60c5-6691-4fd6-8638-589fd95ec8a4@att.net> <vrkabi$233at$1@dont-email.me>
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WM <wolfgang.mueckenheim@tha.de> wrote:
> On 21.03.2025 18:39, Jim Burns wrote:
>> On 3/21/2025 3:50 AM, WM wrote:
>>> On 20.03.2025 23:25, Jim Burns wrote:
>> 
>>>> For sets not.having a WM.size,
>>>> Bob vanishing isn't a size.change.
>>>
>>> Only if reducing isn't reducing.
>> 
>> What you (WM) think is reducing
>> isn't reducing.

> You confuse the clear fact that in the reality of sets vanishing means 
> reducing with the foolish claim that cardinality was a meaningful notion.

> Learn that even Cantor has accepted that the positive numbers have more 
> reality than the even positive numbers.

You mean something like positive numbers have a reality score of 5, and
the even positive numbers only have a reality score of 3?

> He said that is not in conflict with the identical cardinality of both
> sets. And he was right!

I doubt very much Cantor said such rubbish.  He was a mathematician.

> "Coun[t]able" is simply another name for potential infinity.

Not even close.  Countable is an adjective defined in set theory,
"potential infinity" is a fantasy noun, with no place in modern
mathematics.

> Therefore vanishing odd numbers means reducing the reality of the set.

By how much (on our scale of 1 to 10) does this reality get reduced?

> Therefore the sentence "What you (WM) think is reducing isn't
> reducing" exhibits you as a snooty dilettante who cannot distinguish
> between cardinality and reality.

Hah!  He's got to you, has he?  Jim has spent some considerable effort
in trying to get you (WM) to understand about infinite sets.  It would
appear you've failed to learn.  You don't _want_ to learn.  So I suppose
we can expect you to initiate more nonsense threads about sets in the
future.  Not good.

> Regards, WM

-- 
Alan Mackenzie (Nuremberg, Germany).