Timeline for Representing split-complex numbers as intervals and related compactification
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2021 at 17:48 | comment | added | wlad | @Anixx OK, but $\overline{\mathbb R} + i\overline{\mathbb R} \neq P(\mathbb C)$. In fact, I've never seen that before | |
| Dec 14, 2021 at 15:25 | comment | added | Anixx | Well, what I do is considering pairs of $(u,v)$, $u,v\in\overline{\mathbb{R}}$ so this compactification has elements which cannot be represented in $a+bj$ basis, even if we allow $a,b\in\overline{\mathbb{R}}$. | |
| Dec 14, 2021 at 15:21 | comment | added | wlad | Yes, but the difference between this and $P(\mathbb R^2)$ is not to do with the basis | |
| Dec 14, 2021 at 15:16 | comment | added | Anixx | I use $\overline{\mathbb{R}}\times\overline{\mathbb{R}}$ | |
| Dec 14, 2021 at 15:15 | comment | added | wlad | @Anixx en.wikipedia.org/wiki/Projective_line_over_a_ring | |
| Dec 14, 2021 at 15:11 | comment | added | wlad | @Anixx I don't understand what definition of compactification you're using. I'm using the definition of a projective line over a ring, which is basis independent | |
| Dec 14, 2021 at 13:42 | comment | added | Anixx | The compactification with diagnal lines allows to easily generalize functions to this extended set in the diagonal basis. | |
| Dec 14, 2021 at 13:32 | comment | added | Anixx | I would argue that the compactification with lines parallel and perpendicular to the real line is more natural for the complex numbers, and the compactification by adding diagonal lines is more natural for hyperbolic numbers. | |
| Dec 14, 2021 at 13:31 | comment | added | Anixx | The thing is, different basises bring different compactifications. In one basis we add a family of oriented lines, parallel and pependiclar to the real line, in the other we add a family of oriented diagonal lines. | |
| Dec 14, 2021 at 13:17 | history | edited | wlad | CC BY-SA 4.0 |
added 201 characters in body
|
| Dec 14, 2021 at 13:07 | history | edited | wlad | CC BY-SA 4.0 |
added 233 characters in body
|
| Dec 14, 2021 at 13:01 | history | edited | wlad | CC BY-SA 4.0 |
added 233 characters in body
|
| Dec 14, 2021 at 12:55 | history | answered | wlad | CC BY-SA 4.0 |