Re: how

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:
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Le 16/04/2024 à 21:48, Tom Bola a écrit :

WM schrieb:

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Nevertheless the question remains where in the second row is ω located, doesn't it?.

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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.

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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.