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

On 9/18/2024 5:31 PM, Moebius wrote:

Am 18.09.2024 um 21:35 schrieb Chris M. Thomasson:

On 9/18/2024 5:44 AM, WM wrote:

 

Define an interval comprising [exactly] 9182024 points, starting at zero.

>
p0 = (0, 0)
p1 = (1, 0)
pdif = p1 - p0;
pnormal_base = 1.f / 9182024;
>
// add one more point to make it all the way to p1...

 No good idea, since in this case your program will deliver 9182024 + 1 points, right?
 

for (i = 0; i < 9182024 + 1; ++i)
{
    pnormal = pnormal_base * i;
    p2 = p0 + pdif * pnormal;
    plot(p2);
}
>
?

 Nope. The (real) interval [0, 1] consists of more points than just 9182024 (or 9182024 +1).

Of course. However, we can gain any finite granularity we want to simply because it is infinitely dense to being with. :^)
Think of the granularity between the naturals and the unit fractions. Then the reals that are infinitely dense. They are uncountable because they are so dense.

 Actually, of (uncountably) infinitely many points.
 Hint: WM -this fucking asshole full of shit- is always talking nonsense.