Re: Replacement of Cardinality --- infinitesimal number system

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;
}
?