Re: Does the number of nines increase?

Am Tue, 09 Jul 2024 12:08:46 +0000 schrieb WM:

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).

Why this direction of less/greater than?

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

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

Why should there be a smallest element?

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.

"Named", which is all of them.

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.

The only step is at 0.

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Am Fri, 28 Jun 2024 16:52:17 -0500 schrieb olcott:
Objectively I am a genius.