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

On 10/27/24 3:38 AM, WM wrote:

Am 26.10.2024 um 21:35 schrieb Chris M. Thomasson:

On 10/26/2024 9:04 AM, WM wrote:

On 26.10.2024 05:21, Jim Burns wrote:

On 10/25/2024 3:15 PM, WM wrote:

>

Mainly, among other points, the claim that
all unit fractions can be defined and the claim that
a Bob can disappear in lossless exchanges.

>
The proof that all unit fractions can be defined
is to define them
as reciprocals of positive countable.to.from.0 numbers.
>
That describes all of them and only them.

>
No, you falsely assume that all natnumbers can be defined.

>
Huh? Confusing to me. Humm... Are you trying to suggest that a natural number can _not_ be a natural number?

 No. But most natnumbers cannot be defined. This can best be understood by the unit fractions.

So, what is the line between the DEFINED natural numbers and the "not defined"?

 Try to understand the function NUF(x) = Number of Unit Fractions between 0 and x, which starts with 0 at 0 or less and after NUF(x') = 1 cannot change to 2 without pausing for an interval consisting of uncountably many real points. The reason is this: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

And isn't defined, since there is no finite number x, such that NUF(x) has the value of 1.
Your logic just assumes the existance of something that doesn't exist, and thus is unsound, just like your own mind,

 Regards, WM