Re: Contradiction of bijections as a measure for infinite sets

On 4/6/24 9:26 AM, WM wrote:

Le 05/04/2024 à 12:57, FromTheRafters a écrit :

WM explained on 4/4/2024 :

 

Explain why first bijecting n and n/1 should destroy an existing bijection!

>
You still seem to think that sets change. If you mean 'n' is an element of the naturals then of course N bijects with the naturals as embedded in Q.

 Of course. But if someone doubts it, I could directly map the naturals n/1 to the fractions with the result that there is no bijection.

No, not "No Bijection", but that mapping isn't a bijection.
Showing one attempted mapping doesn't form a bijection doesn't show that no bijection exists when working with infinite sets. You are just stuck in your finite thinking.

 

Also, the complement of the naturals over one in Q is the same size as the proper subset you created.

 No, that is disproved by the remaining Os.

Which only shows that this one mapping doesn't work.
And, when you try it within one set, as opposed to between two sets, that you don't understand how it is supposed to work.

 Regards, WM