Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, effectively)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 30. Dec 2024, 09:44:48
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vktmi3$1ia1u$1@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 30.12.2024 01:36, Richard Damon wrote:
On 12/29/24 5:31 PM, WM wrote:
My theorem: Every union of FISONs which stay below a certain threshold stays below that threshold.
Find a counterexample. Don't claim it but prove it. Fail.
But what does that prove?
That proves the existence of dark numbers.
The finite numbers are finite, and that is it.
FISONs do not grow by unioning them. All FISONs and their unions stay below 1 % of ℕ.
Proof: Every FISON that is multiplied by 100 remains a FISON that can be multiplied by 100 without changing this property.
If ℕ is an actually infinite set then it is not made by FISONs.
Regards, WM