Re: Does the number of nines increase?

Le 09/07/2024 à 02:15, Jim Burns a écrit :

On 7/8/2024 3:57 PM, WM wrote:

Le 08/07/2024 à 19:33, Jim Burns a écrit :

 

A change needs be _with respect to_ something,

>
yes, to the value befor that point.

 Yes,
for example, floor(0) with respect to floor(0-ε)
 Or,
yes, to the value after that point

No, my definition _for this concrete case_ is this: A change of NUF(x) happens at point x if for all y < x NUF(x) > NUF(y).

A person who believes in
loss by exchange and
NUF changing at 0

 _near_ 0

So the change does not happen at zero. Thank you for correcting your NUF(x) changes "at" 0. Otherwise you would really have been of no interest to me.

 Does each nonempty set S of unit.fractionsᵂᴹ
hold a largest S.element?

A largest and a smallest. Alas the smallest can only be found if it is not dark.

 Does each unit.fractionᵂᴹ u (including 1)
have a next.smaller unit.fractionᵂᴹ ⅟(1+⅟u) ?

Obviously not, as I have demonstrated irrefutably (refuted only by people who cannot think clear enough. But every unit fraction that can be named has a next smaller unit fraction.

 Does each unit.fractionᵂᴹ v (excluding 1)
have a next.larger unit.fractionᵂᴹ ⅟(-1+⅟v) ?

Yes, but for all dark unit fractions this cannot be found. Every unit fraction excluding 1/1 that can be named has a next larger unit fraction.

 Or is  what you're talking about irrelevant to
what you're saying?

Relevant is this and only this: NUF(0) = 0, and the first step happens at x > 0. Like every step it is a step by 1.
Regards, WM