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Subject: Re: Replacement of Cardinality
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From: WM <wolfgang.mueckenheim@tha.de>
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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