Re: How many different unit fractions are lessorequal than all unit fractions?

Am 15.09.2024 um 02:05 schrieb Chris M. Thomasson:

On 9/14/2024 11:35 AM, joes wrote:

Am Sat, 14 Sep 2024 16:01:02 +0200 schrieb WM:

On 14.09.2024 01:05, FromTheRafters wrote:

WM explained :

>

No, that is your big mistake. In the interval [0, 1] there is a point
next to 0 and a point next to 1, and infinitely many are beteen them.

Define 'next' in this context.

Two points are next to each other means that no point is between them.

Which is the case for no two (different) reals.
>

Two points on the real line that are different from one another have infinite***ly manY*** points between them.

 Indeed: If r,s e IR and, say, r < s, then r < (r + s)/2 < s.
 But then r < (r + s)/2 < ((r + s)/2 + s)/2 < s, and so on (ad infinitum).
 

Two points that are not different are the same point... ;^D

 Indeed (at least in a classical context):
    Ax,y e IR: ~(x =/= y) -> x = y. :-)
 Proof: "x =/= y" is just short for "~(x = y)". Hence ~(x =/= y) just means ~~(x = y). And with /~~elimination/, we get x = y.