Sujet : Re: How many different unit fractions are lessorequal than all unit fractions?
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 01. Oct 2024, 18:29:21
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vdhbhg$2qovr$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 30.09.2024 21:51, Jim Burns wrote:
On 9/30/2024 2:54 PM, WM wrote:
NUF(0) = 0 and NUF(1) = ℵo.
ℵ₀ is the cardinality of
cardinalities which increase by 1
Yes.
If ℵ₀ is any
cardinality which increases by 1
No.
Therefore,
ℵ₀ does not increase by 1.
Yes.
∀n ∈ ℕ: 1/n - 1/(n+1) > 0
shows that at
...no unit.fraction...
no point x NUF can increase by
more than one step 1.
0 is not a unit.fraction.
That proves NUF(0) = 0.
It is fact with your set too.
I am not responsible.
Also,
you are not correct.
What is incorrect?
No reason even to care about
mathematical basic truths like
∀n ∈ ℕ: 1/n - 1/(n+1) > 0 ?
∀n ∈ ℕ: 1/n > 1/(n+1) > 0
∀n ∈ ℕ: 1/n isn't first unit.fraction.
You should understand that NUF cannot increase by more than 1 and cannot start with more than 0 at 0. Do you understand that?
Regards, WM
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