Sujet : Re: Replacement of Cardinality
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.logic sci.mathDate : 14. Aug 2024, 20:04:22
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <eb4a6291-2ee6-4ac1-9892-840896f99b1f@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 8/14/2024 8:28 AM, WM wrote:
Le 13/08/2024 à 19:42, Jim Burns a écrit :
The existence of the smallest unit fractions
is contradictory in the land of
rationals with
countable.to numerators and denominators
with each split situated ==
a last point in the foresplit or
a first point in the hindsplit.
>
The existence of a smallest unit fraction is
the only alternative to the existence of
more than one at a real point.
The NONexistence of a smallest unit fraction is why,
for each unit fraction,
there are infinitely.many smaller unit fractions.
And with no two at one point.
In a finite ordered set,
each non.{} subset has two ends.
For each unit fraction,
its smaller unit fractions have an upper end,
which is that unit fraction,
but a lower end doesn't exist,
the smallest unit fraction doesn't exist.
For each unit fraction,
its smaller unit fractions are one.ended,
they _aren't_ finitely.many.
∀ᴿx > 0: NUF(x) = ℵ₀
because each x > 0 is not above a second end.