Re: how

On 6/11/2024 12:41 PM, Chris M. Thomasson wrote:

On 6/10/2024 4:20 PM, Chris M. Thomasson wrote:

On 6/10/2024 4:09 PM, Moebius wrote:

Am 11.06.2024 um 00:49 schrieb Chris M. Thomasson:

On 6/10/2024 3:47 PM, Moebius wrote:

Am 11.06.2024 um 00:33 schrieb Chris M. Thomasson:
>

Crap, or really bad? What did I miss here?

>
Math? :-)
>

>
I was just thinking about,
>
[1, 2, 3, 4, ...]
>
applied to:
>
[1/2, 2/2, 3/2, 4/2, ...]
>
creates
>
[.5, 1, 1.5, 2, ...]

>
Ummm...
>
[1/2, 2/2, 3/2, 4/2, ...] = [.5, 1, 1.5, 2, ...].
>
Say, in the context of Q or IR (with decinal representation of numbers).
>

Refining to all the naturals we get:
>
[1, 2, ...]

>
What do you "mean" be "refining"? :-P
>
I guess you mean some sort of ""reduction"" (or "filtering").
>
Actually, I've never heard about this (in a math context).

 My programming side. ;^)
 

But it certainly can be defined.

 Yup! It sure can and is interesting to me.
 By the way... Wrt something like:
 0.666...
 is:
 0.(6) better and easier to read?
 

Let's call this operation "nat".
>
Then
>
     nat [.5, 1, 1.5, 2, ...] = [1, 2, ...] .
>
And, say,
>
     nat [.5, 2, 1.5, 7, ...] = [2, 7, ...] .

>
>
For the filter, or refinement, yes. [.5, 2, 1.5, 7, ...] = [2, 7, ...]
>
Indeed.
>

>
Right?
>

Make any sense?

>
Sure.

>

 Therefore:
 nat [-.5, 8/2, 14/3, 5/2, .6(6), 4/2, -7, 5.2, 0+0i, ...] = [4, 2, ...]
 The nat operation seems logical to me. :^)

Or, if somebody desires to treat zero as a natural number the result would be, wrt the 0+0i element,
[4, 2, 0, ...]
Humm...