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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
 (extra-ordinary)
Date: Thu, 12 Dec 2024 14:18:58 -0800
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On 12/12/2024 2:18 PM, Chris M. Thomasson wrote:
> On 12/12/2024 2:11 PM, WM wrote:
>> On 12.12.2024 17:15, Jim Burns wrote:
>>> On 12/12/2024 4:07 AM, WM wrote:
>>
>>> The existence of a bridge implies that,
>>> somewhere we can't see,
>>> a size which cannot change by 1
>>> changes by 1 to
>>> a size which can change by 1
>>
>> Every set can change by one element. No size is required and no size 
>> is possible if this is forbidden.
>>>
>>>> There must be
>>>> a continuous sequence of steps of height 1
>>>> from many elements to none.
>>>
>>> What you describe is many, not infinity.
>>>
>>>> Can you confirm this?
>>>
>>> For many, yes,
>>> For infinity, never.
>>> Having a continuous sequence of steps of height 1
>>> from many elements to none
>>> is what makes it finite.
>>
>> It is needed by Cantors mappings.
> 
> 
> Again, Cantor Pairing works with any natural number. Not just many of 
> them... ALL of them. :^)
> 

Also, when I say all I am not implying some sort of largest natural number.