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 : 01. Nov 2024, 11:37:29
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vg2b17$36ojq$7@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 01.11.2024 00:44, Richard Damon wrote:
On 10/31/24 1:41 PM, WM wrote:
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.

Or, just admit that your NUF(x) is where the contradiction is and drop it.
Why? If alleged sets of real numbers really consist of real numbers, then we can treat them as real points.
Regards, WM

Date Sujet#  Auteur
2 Sep 24 * How many different unit fractions are lessorequal than all unit fractions?2203WM
2 Sep 24 +* Re: How many different unit fractions are lessorequal than all unit fractions?2098Richard Damon
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3 Sep 24 i `* Re: How many different unit fractions are lessorequal than all unit fractions?2091Jim Burns
3 Sep 24 i  `* Re: How many different unit fractions are lessorequal than all unit fractions?2090WM
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