Sujet : Re: How many different unit fractions are lessorequal than all unit fractions?
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 30. Sep 2024, 20:51:54
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <adea0828-b2b1-4273-8e99-8c143f17f4f1@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
User-Agent : Mozilla Thunderbird
On 9/30/2024 2:54 PM, WM wrote:
On 30.09.2024 20:33, Jim Burns wrote:
On 9/30/2024 11:12 AM, WM wrote:
On 29.09.2024 21:56, Jim Burns wrote:
On 9/27/2024 2:54 PM, WM wrote:
On 25.09.2024 20:40, Jim Burns wrote:
There are
numbers (cardinalities) which increase by 1
and other numbers (cardinalities),
which don't increase by 1.
>
No.
>
You invoke _axiom.1_
Every countable set is countable,
i.e., it increases one by one.
What you are talking about aren't _our_ sets.
>
NUF(0) = 0 and NUF(1) = ℵo.
ℵ₀ is the cardinality of
cardinalities which increase by 1
If ℵ₀ is any
cardinality which increases by 1
then ℵ₀+1 is also a
cardinality which increases by 1
and
there are more.than.ℵ₀.many
cardinalities which increase by 1
Contradiction.
Therefore,
ℵ₀ does not increase by 1.
∀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.
It is fact with your set too.
I am not responsible.
Also,
you are not correct.
I only made the discovery.
>
We have no more reason to care about _your_ "sets".
>
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.
Unit fractions do not come into being.
>
But they come into sight.
We reason about existing unit.fractions,
starting with
a description of an existing unit fraction.
Visibility, detectability, etc
are irrelevant to an argument about
_existing_ unit.fractions.
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