Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

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Sujet : Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.math
Date : 02. Nov 2024, 18:38:45
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vg5o35$3s1gf$2@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
User-Agent : Mozilla Thunderbird
On 02.11.2024 13:38, Moebius wrote:
Am 02.11.2024 um 13:17 schrieb joes:
Am Fri, 01 Nov 2024 18:33:34 +0100 schrieb WM:
 
I say: All exist. That implies [a] smallest.
 No, it doesn't.
If NUF(x) has grown to ℵ₀ at x₀, then ℵ₀ unit fractions must be between 0 and x₀. Hence at least ℵ₀ points with ℵ₀ intervals of uncountably many points must be between 0 and x₀. That cannot happen at x₀ = 0.
NUF can grow only one by one.
Regards, WM

Date Sujet#  Auteur
2 Sep 24 * How many different unit fractions are lessorequal than all unit fractions?2203WM
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