Re: Contradiction of bijections as a measure for infinite sets

Le 06/04/2024 à 22:03, Richard Damon a écrit :

On 4/6/24 3:40 PM, WM wrote:

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.y

 But he DOES, as he talks about the two SETS of numbers that are matched up.

One set and its subset. Dedekind: A system S is said to be /infinite/ if it is similar to a real part of itself. To consider them as two sets does not change the numbers of elements.

 And yes, the size of the set of all fractions is EXACTLY of the same size as the set of all Prime Numbers, and that size is Aleph_0.

Wrong. Proof: All prime numbers p are fractions p/1 ∈ ℚ, but 1/2 is not prime.
Regards, WM