Re: Contradiction of bijections as a measure for infinite sets

Le 06/04/2024 à 15:40, Richard Damon a écrit :

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.

That mapping is Cantor's proposal. But for every other mapping, the O's would also remain. All O's! It is th lossless exchange which proves it.

 No, that is disproved by the remaining Os.

 Which only shows that this one mapping doesn't work.
 

It is Cantor's famaous mapping, more than a century believed to be a bijection.

And, when you try it within one set, as opposed to between two sets,

If it operates, it must operate within one set too.
Regards, WM