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 : 31. Oct 2024, 18:41:36
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vg0fgh$2ppbe$1@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
User-Agent : Mozilla Thunderbird
On 31.10.2024 13:22, Jim Burns wrote:
On 10/31/2024 4:13 AM, WM wrote:

Neither
  ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
nor
  ∀ᴿx > 0: ∀n ∈ ℕ: ⅟⌈n+⅟x⌉ ∈ ⅟ℕ∩(0,x]
is wrong.
>
But the first formula predicts that
only single unit fractions
are existing on the real line.
How could NUF(x) grow from zero by more than 1?
 Is
⎛  ∀ᴿx > 0:
⎜  ∀n ∈ ℕ:
⎝ ⅟⌈n+⅟x⌉ ∈ ⅟ℕ∩(0,x]
wrong?
One of two contradicting formulas must be dropped.
Regards, WM

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