Sujet : Re: Replacement of Cardinality
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.logic sci.mathDate : 17. Aug 2024, 22:39:30
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <c4bbc4d3-26b3-4e53-9c82-87c8396d155d@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 8/17/2024 9:28 AM, WM wrote:
Le 16/08/2024 à 19:39, Jim Burns a écrit :
no element of ℕᵈᵉᶠ is its upper.end,
because
for each diminishable k
diminishable k+1 disproves by counter.example
that k is the upper.end of ℕᵈᵉᶠ
>
SBZ(x) starts with 0 at 0 and increases,
but at no point x it increases by more than 1
because of
∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
Therefore there is a smallest unit fractions and vice versa a greatest natnumber.
What can't you understand?
How can ½⋅β
⎛ half the allegedly.positive greatest.lower.bound β of
⎝ visibleᵂᴹ.unit.fractions
be both lower.bound ( ½⋅β < β)
and not.lower.bound ( 2⋅β > ⅟k and ½⋅β > ¼⋅⅟k)
of the visibleᵂᴹ.unit.fractions?
…