Newsportal USENET - Re: How many different unit fractions are lessorequal than all unit fractions?

Sujet : Re: How many different unit fractions are lessorequal than all unit fractions?
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.math
Date : 23. Sep 2024, 13:57:07

Autres entêtes

Organisation : A noiseless patient Spider
Message-ID : <vcroj3$2nfvb$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
User-Agent : Mozilla Thunderbird

On 22.09.2024 22:22, Jim Burns wrote:
> On 9/22/2024 2:37 PM, WM wrote:
>> On 22.09.2024 19:44, Jim Burns wrote:
>
>>> There is no point next to 0.
>
>> There is a smallest unit fraction
>> because
>> there are no unit fractions without a first one
>> when counting from zero.
>
> Each visibleᵂᴹ unit.fraction ⅟k has
> a counter.example ¼⋅⅟k to its being smallest.
Yes. Therefore the smallest unit fraction must be dark.
> No positive point, unit.fraction or otherwise,
> is NOT undercut by some visible unit fraction.
Wrong. NUF(x) grows from 0 to more. This increase cannot avoid 1 because of ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
Regards, WM

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