Re: Contradiction of bijections as a measure for infinite sets

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.