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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Thu, 19 Sep 2024 14:27:41 -0700
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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.
>