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 : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.math
Date : 31. Oct 2024, 01:14:19
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <7def94cc-4a51-4305-8e62-0c5b5f5a6b0a@att.net>
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
User-Agent : Mozilla Thunderbird
On 10/30/2024 3:55 PM, WM wrote:
On 30.10.2024 18:05, Jim Burns wrote:

∀ᴿx > 0: ∀n ∈ ℕ: ⅟⌈n+⅟x⌉ ∈ ⅟ℕ∩(0,x]
>
∀ᴿx > 0: NUF(x) = |ℕ|
>
Is ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 wrong?
Neither
  ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
nor
  ∀ᴿx > 0: ∀n ∈ ℕ: ⅟⌈n+⅟x⌉ ∈ ⅟ℕ∩(0,x]
is wrong.

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