Sujet : Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.mathDate : 02. Nov 2024, 13:28:57
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vg55u9$3pkpk$1@dont-email.me>
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Am 02.11.2024 um 13:11 schrieb joes:
Am Sat, 02 Nov 2024 10:59:04 +0100 schrieb WM:
If all unit fractions are existing, then a smallest unit fraction is
existing.
Invalid deduction.
Actually, no _deduction_ at all.
It's just a nonsensical or false "implication".
Either
<nonsensen> -> <a false statement>
or
<a true statement> -> <a false statement> .
Are we willing to consider "all unit fractions are existing" a meaninful (and even true) statement? What would it mean for a unit fraction not to exist?
Mückenheim ist für jede Art von Mathematik zu doof und zu blöde.
Anyway, we may safely replace his claim with the FALSE claim:
"There is a smallest unit fraction." (WM)
In fact, there isn't such a unit fraction.
Proof: If u is a unit fraction, 1/(1/u + 1) is a smaller one. qed