Sujet : Re: Contradiction of bijections as a measure for infinite sets
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 27. Mar 2024, 19:54:37
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <36a016ab-d51a-45e0-a1b7-5170955c824f@att.net>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Mozilla Thunderbird
On 3/27/2024 9:38 AM, WM wrote:
Le 26/03/2024 à 16:40, Jim Burns a écrit :
ℕ and ℚ have the same infinity.
>
Only if
logic (every lossless exchange is lossless)
is violated and damaged, i.e.,
only in matheology.
ℕ and ℚᶠʳᵃᶜ are larger than each set which is
not the same size as any subset or superset.
Therefore,
ℕ and ℚᶠʳᵃᶜ are not sets which are
not the same size as any subset or superset.
k ∈ ℕ
k ⟼ iₖ/jₖ
sₖ = max{h: (h-1)(h-2/2 < k }
iₖ = k-(sₖ-1)(sₖ-2)/2
jₖ = sₖ-iₖ
iₖ/jₖ ∈ ℚᶠʳᵃᶜ
iₖ/jₖ ∈ ℚᶠʳᵃᶜ
iₖ/jₖ ⟼ kᵢₖⱼₖ
sᵢₖⱼₖ = iₖ+jₖ
kᵢₖⱼₖ = (sᵢₖⱼₖ-1)(sᵢₖⱼₖ-2)/2+iₖ
kᵢₖⱼₖ ∈ ℕ
kᵢₖⱼₖ = k
ℕ and ℚᶠʳᵃᶜ are the same size.
…