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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 1 Dec 2024 15:19:04 -0800
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On 11/29/2024 5:44 PM, Jim Burns wrote:
> On 11/29/2024 4:29 PM, WM wrote:
>> On 29.11.2024 21:54, Jim Burns wrote:
>>> On 11/29/2024 2:37 PM, WM wrote:
>>>> On 29.11.2024 19:08, Jim Burns wrote:
> 
>>>>>
>>
>> JB contradicting himself:
>>
>>> After all the swaps
>>>  (of which no swap is a change in cardinality)
>>> what remains is a proper subset
>>>  (which is not a change in cardinality).
> 
> I (JB) contradict the finiteness of
> the set of all finite cardinals.
> Nothing more than that.
> 
> Change a set having a finite cardinality by 1.
> The new set has a changed cardinality.
> (This is essentially what 'finite cardinal' means).
> 
> The set of finite cardinalities,
> for any finite cardinal,
> includes more than that cardinal.
> Each finite cardinal is not the one that set has.
> 
> Change the set of finite cardinalities by 1.
> The new set has NOT changed cardinality.
> The sets do not have any of
> the cardinalities which would change.
> The sets have a different cardinality,
>   one which does not change when the set changes.
> 
> 
> After all the swaps
>   (of which no swap is a change in cardinality)
> what remains is a proper subset
>   (which is not a change in cardinality).
> Because infinite.
> 
> 

Infinite finite sets:

{ { 1 }, { 1, 2 }, { 1, 2, 3 }, { 1, 2, 3, 4 }, ... }

?