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.

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