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Subject: Re: Contradiction of bijections as a measure for infinite sets
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From: WM <wolfgang.mueckenheim@tha.de>
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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