Sujet : Re: Replacement of Cardinality
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logic sci.mathDate : 30. Jul 2024, 18:30:17
Autres entêtes
Organisation : Nemoweb
Message-ID : <P04FAosjolyjDfgV0JPXWx1mF6o@jntp>
References : 1 2 3 4 5 6
User-Agent : Nemo/0.999a
Le 29/07/2024 à 20:33, Jim Burns a écrit :
On 7/29/2024 9:23 AM, WM wrote:
NUF(x) cannot grow by more than 1 at any x.
NUF(x) = |⅟ℕ∩(0,x]|
NUF(x) cannot grow by more than 1 at any x > 0
Correct. At x < 0 or x = 0 NUF(x) = 0 and remains so.
¬(0 > 0)
Correct.
⅟ℕ∩(0,x] has
each non.{}.subset maximummed
each unit.fraction down.stepped
each non.maximum up.stepped
and therefore
ℵ₀.many unit.fractions
x > 0 ⇒ NUF(x) = ℵ₀
That implies a growth between [0, 1] and (0, 1].
Between [0, 1] and (0, 1] NUF(x) cannot grow because no unit fraction fits in between.
Strange how void of logical thinking matheologians are.
Regards, WM
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