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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality --- infinitesimal number system
Date: Tue, 30 Jul 2024 17:29:18 -0700
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On 7/30/2024 5:11 PM, olcott wrote:
> On 7/30/2024 6:54 PM, Moebius wrote:
>> Am 31.07.2024 um 01:46 schrieb olcott:
>>> On 7/30/2024 5:49 PM, Moebius wrote:
>>>> Am 30.07.2024 um 20:37 schrieb Jim Burns:
>>>>> On 7/30/2024 1:30 PM, WM wrote:
>>>>
>>>>>> [...] between [0, 1] and (0, 1].
>>>>
>>>> Could you please explain to me the meaning of the phrase "between 
>>>> [0, 1] and (0, 1]"?
>>>
>>> One can construe them as line segments that differ in length
>>> by a single geometric point on the number line. I came up
>>> with that a few years ago with my infinitesimal number system
>>> that <bla>
>>
>> Hint: IR does not comtain any "infinitesimal numbers" (except 0 that is).
> 
> It is the case that the infinite set of points specified
> by [0, 1] has exactly one less point than the infinite
> set of points specified by (0, 1].
> 

You mean going from:

p0 = {-1, 0};
p1 = {1, 0};
dif = p1 - p0;
unsigned long n = 10;

float normal_base = 1.f / n;

vs:


float normal_base = 1.f / (n - 1);

as in:

for (unsigned long i = 0; i < n; ++i)
{
     float normal = normal_base * i;

     glm::vec2 k0 = p0 + dif * normal;
}

?