Sujet : Re: Replacement of Cardinality
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logicDate : 30. Jul 2024, 18:37:09
Autres entêtes
Organisation : Nemoweb
Message-ID : <nhZZyv1rDmL90pLuaDma-8md3qw@jntp>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Nemo/0.999a
Le 30/07/2024 à 03:18, Richard Damon a écrit :
On 7/29/24 9:11 AM, WM wrote:
But what number became ω when doubled?
ω/2
No, that is w double, what number in the first set became w?
>
Every natural number when doubled is a Natural Number.
No.
Why not? WHich ones don't?
ω/2 and larger.
Note, ω-1 doesn't exist in the base transfinite numbers, just as -1 doesn't exist in the Natural Numbers, you can't go below the first element.
If all natural numbers exist, then ω-1 exists.
Why?
Because otherwise there was a gap below ω.
That is unavoidable. You believe in the magical appearance of infinitely many unit fractions. That breaks logic and mathematics.
Nope,
∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Note the u niversal quantifier.
Regards, WM
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