Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 08.01.2025 00:30, Richard Damon wrote:

On 1/7/25 7:51 AM, WM wrote:

No, ZF doesn't have as an axiom that the set of Natural Numbers exist.

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AoI: There exists an infinite set S.

 Which isn't that the NATURAL NUMBERS are an infinite set.

The infinite set has been designed by Zermelo according to Dedekind's definition of the natural numbers, as Zermelo noted. https://gdz.sub.uni-goettingen.de/id/PPN235181684_0065?tify=%7B%22pages%22%3A%5B276%5D%2C%22pan%22%3A%7B%22x%22%3A0.461%2C%22y%22%3A1.103%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.884%7D

Every union of FISONs {1, 2, 3, ..., n} which stay below this threshold stays below this threshold too.

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But not the union of *EVERY* FISON, the FULL INFINITE set of them.

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All are below 1 %.

 No,

Show one FISON that is larger than 1 %.

 So, all you prove is that a finite subset of an infinite set doesn't cover all of the infinite set.
 Your logic can't handle *EVERY* FISON at once.

Show one FISON that is larger than 1 %.
Regards, WM

 

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SOething your "logic" can't handle,

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Luckily.

 So, you think you are "lucky" to be ignorant?
 I guess that just shows how your logic works.
 

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Regards, WM
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