Sujet : Re: The set of necessary FISONs
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 12. Mar 2025, 21:18:47
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vqsq78$2p6pb$3@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 12.03.2025 21:12, FromTheRafters wrote:
WM wrote on 3/12/2025 :
Inductive sets do not contain dark numbers.
Is the set of natural numbers an inductive set?
The set of definable natural numbers or FISONs is an inductive set and like every inductive set it is potentially infinite.
ℕ \ {1} = ℵo,
and if ℕ \ {1, 2, 3, ..., n} = ℵo
then ℕ \ {1, 2, 3, ..., n+1} = ℵo.
The set of FISONs satisfying this definition is without end. It has no greatest element. But it does not contain all natural numbers. ℵo always remain.
If its union UF = ℕ then Ø = ℕ.
Regards, WM