Re: how

On 4/25/24 4:27 PM, WM wrote:

Le 25/04/2024 à 21:47, Moebius a écrit :

Am 25.04.2024 um 21:40 schrieb WM:

Le 24/04/2024 à 19:40, Moebius a écrit :

Am 24.04.2024 um 19:01 schrieb WM:
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What is between ω and ω*2?

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Was wohl, Du Hirni? Wenn wir von Ordinalzahlen reden, dann gilt:
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ω < ω+1 < ω+2 < ... < ω+ω = ω*2
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Die Menge der Ordinalzahlen, die zwischen ω und ω*2 liegen, ist also
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{o e ORD : ω < o < ω*2} = {ω+1, ω+2, ω+2, ...}.
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Übrigens enthält diese Menge aleph_0 Ordinalzahlen

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every second of which is in [...] (0, ω)*2.

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None of which is in (0, ω)*2, since (0, ω)*2 c (0, ω)

 Nonsense.
The complete set is enlarged by doubling.
 Regards, WM
 

But the "Size" of the set is Aleph_0, and 2*Aleph_0 = Aleph_0, so it "enlarged" to be the same size it was before.
That is how the math of transfinite Cardinal numbers work.
It may break your logic, because your logic only handles finite numbers, and blows itself up when pushed past that.