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

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.

Almost all unit fractions
cannot be discerned by definable real numbers.

>
All unit fractions are reciprocals of
positive countable.to.from.0 numbers.

>
That does not change the facts.

 Clearly, the disagreement of proofs
does not change which claims you call facts.

Try to define more unit fractions than remain undefined.
Try to understand the function NUF(x) which starts with 0 at 0 and after 1 cannot change to 2 without pausing for an interval consisting of uncountably many real points.

Don't you claim that
every unit fraction can be discerned, i.e. separated from the smaller ones by a real number?

 ½⋅(⅟n+⅟(n+1)) existing is discerning?
I did not know that.

Giving a real number _by its digits or as a fraction_ which is between two unit fractions discerns the larger one and its larger predecessors.
Regards, WM