Sujet : Re: How many different unit fractions are lessorequal than all unit fractions?
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 02. Oct 2024, 12:10:09
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vdj9mg$3713m$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
User-Agent : Mozilla Thunderbird
On 01.10.2024 22:05, Jim Burns wrote:
On 10/1/2024 1:29 PM, WM wrote:
>
What is incorrect?
This is incorrect:
🛇⎛ ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 shows that
🛇⎜ at no point x
🛇⎝ NUF can increase by more than one step 1.
∀n ∈ ℕ: 1/n - 1/(n+1) > 0 doesn't show that.
You believe that more than one unit fractions can occupy one and the same point nevertheless? That would make the distance 0, but it is > 0. Therefore you are wrong.
∀n ∈ ℕ: 1/n - 1/(n+1) > 0 shows
∀n ∈ ℕ: 1/n > 1/(n+1) > 0
which shows
each unit fraction 1/n is not first.
No. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 does not prove that n+1 is a natural number. Note the infinite sequence
1, 2, 3, ..., ω-2, ω-1, ω.
It consists of infinitely many finite numbers.
Regards, WM
…