Re: Contradiction of bijections as a measure for infinite sets

Le 07/04/2024 à 13:16, Richard Damon a écrit :

On 4/7/24 4:32 AM, WM wrote:

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.

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

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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

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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.

  But does affect your logic of pairing.

No. Since there are precisely as many natnumbers n as natnumber fractions n/1, nothing is affected. The only effect is that the Os can be proven to remain the same number in every step. This is true in all mappings but more easily seen in mine.

So, With infinite sets, a proper subset CAN be the same size as its parent.

Impossible.

 You are just PROVING you don't understand how infinity works,

I understand that a crowd of fools has been tricked by Cantor.
Regards, WM