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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions?
Date: Tue, 01 Oct 2024 17:11:06 -0400
Organization: Peripheral Visions
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Chris M. Thomasson wrote :
> 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.

It is 'never' a circle.

https://www.craig-wood.com/nick/articles/pi-archimedes/