Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logicDate : 16. Dec 2024, 12:28:52
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vjp2tl$12v74$2@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 16.12.2024 11:23, Mikko wrote:
On 2024-12-15 11:33:15 +0000, WM said:
>
We cannot name dark numbers as individuals.
We needn't. The axioms of natural numbers ensure that every natural number
has a successor,
The set, i.e. all numbers together, has no successor. That is a necessary condition for using all with no exception. That must happen according to
∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}.
If that is not possible then there are no
natural numbers.
That is not possible for an actually infinite set. It is only possible for numbers coming into being.
Regards, WM
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