Re: Contradiction of bijections as a measure for infinite sets

Le 27/03/2024 à 18:54, Jim Burns a écrit :

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 the same size.

ℕ and ℕ are the same size.
ℚ and ℚ are the same size.
Removing a proper fraction decreases ℚ but leaves it larger than ℕ. When the size changes it cannot remain the same.
Showing a not bijection proves different sizes of sets.
Why is that more meaningful than Cantor's bijections?
 Between infinite sets there cannot exist any mapping because most elements are dark. But we can assume that very simple mappings like f(x) = x are true even for dark elements.
 Therefore between the rational numbers and the natural numbers f(n) = n/1 can be accepted, also f(n) = 1/n, but not f(n) = 2n.
 Regards, WM
Regards, WM