Sujet : Re: Replacement of Cardinality
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.logic sci.mathDate : 12. Aug 2024, 19:34:33
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <7283ed38-26be-4ded-9dc1-ba879c881fe8@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 8/12/2024 9:47 AM, WM wrote:
Le 11/08/2024 à 19:56, Jim Burns a écrit :
On 8/11/2024 10:09 AM, WM wrote:
And end is there, or before the point,
after which no elements follow.
>
⎛ Something not.in a set cannot be
⎜ an end of the set,
⎜ although it might be a bound of the set.
>
Before the bound there is the end,
perhaps dark.
No.
0 is
greatest.lower.bound β of visibleᵂᴹ unit.fractions
otherwise,
½⋅β is both lower.bound and not.lower.bound
0 not a visibleᵂᴹ unit.fraction.
No point ε > 0 is the end of
visibleᵂᴹ.or.darkᵂᴹ unit.fractions.
⎛ Assume otherwise.
⎜ Assume ε > 0 is the end of
⎜ visibleᵂᴹ.or.darkᵂᴹ unit.fractions.
⎜
⎜ ε > 0 is a lower.bound of
⎜ visibleᵂᴹ.or.darkᵂᴹ unit.fractions.
⎜
⎜ ε > 0 is a lower.bound of
⎜ the visibleᵂᴹ unit.fractions.
⎜
⎜ However
⎜ 0 is
⎜ greatest.lower.bound of visibleᵂᴹ unit.fractions
⎝ Contradiction.
Therefore,
no point ε > 0 is the end of
visibleᵂᴹ.or.darkᵂᴹ unit.fractions.
…