Re: how

On 6/16/2024 12:05 PM, Chris M. Thomasson wrote:

On 6/16/2024 7:21 AM, WM wrote:

Le 14/06/2024 à 23:43, Moebius a écrit :

"But never two (different) unit fractions at the same coordinate."
>
Well, it's hard to see why he feels the need to express this triviality.

>
Your statement is the reason: Before every x > 0 there are many unit fractions. It is wrong since there would be no no different x to distinguish them.

 Wrt unit fractions... Say, unit_fraction_n = 3:
 unit_fraction[1] = 1/1
unit_fraction[2] = 1/2
unit_fraction[3] = 1/3
unit_fraction[unit_fraction_n] = 1 / unit_fraction_n
... on and on ... :^)
 So, take unit_fraction[3], there are two unit_fraction's "before" it: unit_fraction[2] and unit_fraction[1]... Right?
 Once I explicitly define unit_fraction_n = 3, that is a "finite" point to start to do things, so to speak... Keep in mind that this discussion is "strictly" about unit fractions, right?
 

To alter the realm... Now one can say, hummm, take unit_fraction[2] at 1/2. Have some fun:
1/4 + 1/4 = 1/2
That is breaking 1/2 apart into multiple unit fractions. How about:
1/4 + (1/8 * 2) = 1/2
(1/8 * 2) + (1/16 * 2) * 2 = 1/2
on and on... ;^)