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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, effectively)
Date: Thu, 02 Jan 2025 17:40:51 -0500
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Richard Damon brought next idea :
> On 1/2/25 12:30 PM, WM wrote:
>> On 02.01.2025 14:37, FromTheRafters wrote:
>>> WM was thinking very hard :
>>>> On 01.01.2025 03:03, Richard Damon wrote:
>>>>
>>>>> Yes, SOME of the properties of the set come from properties of its 
>>>>> members,
>>>>
>>>> What property does not?
>>>
>>> Size, for one thing.
>> 
>> Size is the number of elements.
>> 
>> Regards, WM
>
> WHich is a property of the set, but not the individual members.

I would say the opposite. The figures representing natural numbers are 
composed of sub-infinite cardinalities (finite cardinality/number of 
elements), it is the whole collection which is infinite cardinality 
(infinite cardinality/size).

This according to the Von Neumann construction of ordinals of course. 
However, WM simply dismisses out of hand that which he disagrees with, 
cardinality being one of the things he throws out, yet uses unknowingly 
in his so-called proofs.