Re: Replacement of Cardinality

On 8/20/2024 12:35 PM, Chris M. Thomasson wrote:

On 8/19/2024 1:55 PM, FromTheRafters wrote:

Chris M. Thomasson formulated the question :

On 8/18/2024 2:15 PM, Ross Finlayson wrote:

On 08/18/2024 11:52 AM, Chris M. Thomasson wrote:

On 8/18/2024 1:16 AM, joes wrote:

Am Sat, 17 Aug 2024 13:39:52 +0000 schrieb WM:

Le 16/08/2024 à 20:11, joes a écrit :

Am Fri, 16 Aug 2024 17:00:26 +0000 schrieb WM:

Le 16/08/2024 à 18:50, joes a écrit :

Am Fri, 16 Aug 2024 16:19:17 +0000 schrieb WM:

>

Taking steps only until the next unit fraction, you never reach 0.

Start from x = 0. The increase cannot be more than 1.

No, you were counting down from 1.

There we see that counting down to 0 requires dark numbers.

Counting down from infinity is not possible. Your "dark" numbers
are a nonstandard extension.
>

>
Yup. Counting down from infinity is moronic. No wonder why WM assumes
there is a place to start counting from, aka finite...

>
Hey, it was Cantor's idea first, ....
>
>

>
Do you even now how to make a Cantor Set Fractal?

>
Isn't there enough division in here already? :D

 Good one! ;^D

Say, thirds, aka 1 / 3...
https://ibb.co/ZK99d9x
Just typed this out to see if I could do one from scratch! lol. Great fun.
____________________
namespace ct_cantor_play
{
     void
     iterate_0(
         ct::plot::cairo::plot_2d& scene,
         unsigned long ri,
         unsigned long rn,
         glm::vec2 p0,
         glm::vec2 p1
     ) {
         if (ri > rn) return;
         float ri_normal = ri / (float)rn;
         glm::vec2 pdif = p1 - p0;
         glm::vec2 pperp = { -pdif.y, pdif.x };
         float pscale = 1.f / 3.f;
         float gscale = 1.f / 6.f;
         scene.line(p0, p1, CT_RGBF(1 - ri_normal, ri_normal, 1), 5);
         glm::vec2 c0 = p0;
         glm::vec2 c1 = p0 + pdif * pscale;
         glm::vec2 c2 = p1 - pdif * pscale;
         glm::vec2 c3 = p1;
         glm::vec2 b0 = c0 + pperp * ri_normal;
         glm::vec2 b1 = c1 + pperp * ri_normal;
         glm::vec2 b2 = c2 + pperp * ri_normal;
         glm::vec2 b3 = c3 + pperp * ri_normal;
         {
             iterate_0(scene, ri + 1, rn, b0, b1);
             iterate_0(scene, ri + 1, rn, b2, b3);
         }
     }
     void
     manifest(
         ct::plot::cairo::plot_2d& scene
     ) {
         std::cout << "ct_cantor_play::manifest()\n\n";
         {
             {
                 //iterate_0(scene, 0, 5, { -1, 0 }, { 1, 0 });
             }
             {
                 iterate_0(scene, 0, 5, { -1, 0 }, { 1, 0 });
                 iterate_0(scene, 0, 5, { 1, 0 }, { 0, 1 });
                 iterate_0(scene, 0, 5, { 0, 1 }, { -1, 0 });
             }
             {
                 iterate_0(scene, 0, 5, { 1, 0 }, { -1, 0 });
                 iterate_0(scene, 0, 5, { 0, 1 }, { 1, 0 });
                 iterate_0(scene, 0, 5, { -1, 0 }, { 0, 1 });
             }
         }
     }
}
____________________