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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The
 non-existence of "dark numbers"]
Date: Mon, 24 Mar 2025 01:02:43 +0100
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Am 23.03.2025 um 23:19 schrieb Alan Mackenzie:
> Moebius <invalid@example.invalid> wrote:
>> Am 23.03.2025 um 22:28 schrieb Alan Mackenzie:
> 
>>> What is the "reality" (in this sense) of N?
> 
>> The "reality" (or rather "substance") of N are its elements
> 
>>        1, 2, 3, ...
> 
>> Clearly, IN\{1} has less "substance" than IN. Actually, the element 1 is
>> missing in IN\{1} (in comparison to IN).
> 
> Are you sure?

Well, I'm just talking. But it seems to me that Cantor thought along 
these lines.

Clearly, a dead end, of course.

> You seem to be implying that ...

I'm sorry! I just tried to follow Cantor's thoughts. [Not my way of 
thinking.]

> WM seemed to be saying that the "reality"/"substance" of any two sets
> could be ranked, with one greater than the other 

if on is a subset of the other. :-P

Ok, let's try to define it:

A set Y has /more reality/ than a set X if

       X is a PROPER subset of Y.

> I doubt very much that Cantor intended "Realität" to have a mathematical
definition.

Agree. But see above.

> He was merely using the term in an effort to get others to
understand how two sets, one a subset of the other, could have the same
cardinality.

Agree.

You know, he didn't use that "notion" in his _mathematical_ articles.t" 
to have a mathematical
> definition.  He was merely using the term in an effort to get others to
> understand how two sets, one a subset of the other, could have the same
> cardinality.
>