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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)
Date: Tue, 07 Jan 2025 15:08:50 -0500
Organization: Peripheral Visions
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WM was thinking very hard :
> On 07.01.2025 15:05, FromTheRafters wrote:
>> WM wrote :
>>> On 07.01.2025 10:51, FromTheRafters wrote:
>>>
>>>> First several von Neumann ordinals
>>>
>>> v. Neumann was bright but not bright enough.
>>> Why should we use the nomenclature of his disproven theory?
>> 
>> Disproven?
>> 
>>>> 0     =     {}     =     ∅
>>>> 1     =     {0}     =     {∅}
>>>> 2     =     {0,1}     =     {∅,{∅}}
>>>> 3     =     {0,1,2}     =     {∅,{∅},{∅,{∅}}}
>>>> 4     =     {0,1,2,3}     =     {∅,{∅},{∅,{∅}},{∅,{∅},{∅,{∅}}}}
>>>> =====================================
>>>>
>>>> Notice they start at zero (emptyset)
>>>
>>> It would be more important to reach the full set.
>> 
>> It does, in the infinite union.
>
> It does not because the infinite union cannot be larger than every unioned 
> FISON.

Just because you saya so?

> Every unioned FISON is smaller than any definable fraction of the full 
> set ℕ.

So what?