Sujet : Re: Contradiction of bijections as a measure for infinite sets
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 25. Mar 2024, 20:38:01
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <4d225827-f5f9-4f8b-b607-1be3ff16b48b@att.net>
References : 1 2 3 4
User-Agent : Mozilla Thunderbird
On 3/25/2024 7:10 AM, WM wrote:
Le 24/03/2024 à 22:02, Dieter Heidorn a écrit :
[...]
>
Important is only this:
You cannot add a natural number to the set ℕ.
not.exists finiteⁿᵒᵗᐧᵂᴹ ordinal n not.in ℕ
not.exists finiteⁿᵒᵗᐧᵂᴹ ordinal n such that
⟦0,n⟧ not.fits ℕ
== not.exists 1.to.1.map ⟦0,n⟧ ⇉ ℕ
for each finiteⁿᵒᵗᐧᵂᴹ set S
exists finiteⁿᵒᵗᐧᵂᴹ ordinal n such that
⟦0,n⟧ not.fits S
== not.exists 1.to.1.map ⟦0,n⟧ ⇉ S
ℕ is not finiteⁿᵒᵗᐧᵂᴹ.
for each finiteⁿᵒᵗᐧᵂᴹ set S
not.exists 1.to.1.map S∪{Bob} > S
ℕ is not finiteⁿᵒᵗᐧᵂᴹ
for not.finiteⁿᵒᵗᐧᵂᴹ ℕ
exists 1.to.1.map ℕ∪{Bob} ⇉ ℕ
You can add Bob to ℕ
…