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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: how
Date: Wed, 17 Apr 2024 19:26:25 -0400
Organization: i2pn2 (i2pn.org)
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On 4/17/24 4:30 PM, WM wrote:
> Le 17/04/2024 à 21:38, Tom Bola a écrit :
>> WM drivels bullshit again and again, as always:
>>
>>> Le 16/04/2024 à 21:48, Tom Bola a écrit :
>>>> WM schrieb:
>>>
>>>>> Nevertheless the question remains where in the second row is ω 
>>>>> located, doesn't it?.
>>>>
>>>> NOPE - because w is not in the IMAGE of your f(ord) = 2*ord
>>> ω*2 is present. Therefore ω or the ordinals next to it must be 
>>> localized below.
>>
>> Also, 2, 4, 6, ... are present in the image but not 1, 2, 3, ...
> 
> If you accept set theory, then you have to accept too that there is no 
> ordinal between ℕ and ω. The interval populated by ℕ  is (0, ω). By 
> doubling the number of elements remains the same, but the populated 
> interval is (0, ω2) with ω amidst.
> 
> I do not claim that ω is in the image, but it is amidst the interval. 
> That proves that doubled numbers surpassed it.
> 
> Regards, WM

Only the ω doubled passed it. The rest stayed below ω, and no natural 
number doubled isn't a natural number.