Re: Contradiction of bijections as a measure for infinite sets

Le 06/04/2024 à 15:58, Richard Damon a écrit :

On 4/6/24 9:55 AM, WM wrote:

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.

 Cantor's proposal is between members of two distinct sets.

No. He does not specify that. And there is no reason to do so, except that it can be used to contradict the ridiculous nonsense that there are as many fractions as prime numbers.
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It is Cantor's famaous mapping, more than a century believed to be a bijection.

 But HIS does work, when you do it right.

No, his bijection works only for potential infinity applying the "...". I show that his mapping does not work for the complete actually infinite sets. He uses "and so on". Why does any intelligent mind believe that? I show that the remainder will never decrease. There is no belief required. It is provable fact.

 

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

 Why?

Because there are as many naturals in ℕ as in ℚ. Precisely as many. But only my approach shows that they are less than the fractions.
Regards, WM