Re: How many different unit fractions are lessorequal than all unit fractions?

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.