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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: Tue, 1 Oct 2024 11:39:45 -0700
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On 10/1/2024 6:28 AM, FromTheRafters wrote:
> Chris M. Thomasson wrote :
>> On 9/30/2024 4:13 AM, Richard Damon wrote:
>>> On 9/29/24 3:16 PM, WM wrote:
>>>> On 28.09.2024 14:58, Richard Damon wrote:
>>>>> On 9/27/24 3:06 PM, WM wrote:
>>>>>> On 25.09.2024 19:12, Richard Damon wrote:
>>>>>>
>>>>>>> The problem is that it turns out the NUF(x) NEVER actually 
>>>>>>> "increments" by 0ne at any finite point, it jumps from 0 to 
>>>>>>> infinity (Aleph_0) in the unboundedly small gap between 0 and all x
>>>>>>> > 0,
>>>>>>
>>>>>> How do you distinguish them?
>>>>>
>>>>> They have different values, so why can't you?
>>>>
>>>> Then distinguish the first one.
>>>>
>>>> Regards, WM
>>>
>>> There isn't a first one.
>>>
>>> Show me a circle with 4 sides.
>>
>> ;^) Humm, an n-gon where n is taken to infinity is a circle?
> 
> As n goes to infinity, the angle of the vertices goes to 180 degrees -- 
> is a straight line a circle?

No. As n goes to infinity it makes a circle. Think of a finite view of a 
"large" number for n:
_________________________
n = 696969

normal_base = 1.f / n;

for (i = 0; i < n; ++i)
{
     normal = normal_base * i;
     angle = pi2 * normal;

     p0 = { cos(angle), sin(angle) };

     plot(p0);
}
_________________________

I typed this in the newsreader, so sorry for any typos! This a finite 
view of a unit circle. Not a line.

Take n to infinity, well, its a circle...

Taking an n-gon to infinity is a circle.