Timeline for Regarding definition of convex cone and apex
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2022 at 12:38 | comment | added | Sam Hopkins | Sorry, I should have written "the half-plane $\{(x,y)\colon x \geq 0\}$" in the previous comment, of course. | |
| Apr 3, 2022 at 17:22 | comment | added | user332905 | Ok. Thank you.. | |
| Apr 3, 2022 at 17:21 | comment | added | Sam Hopkins | In $\mathbb{R}^2$, the half-plane $\{(x,0)\colon x \geq 0\}$ has all of the line $x=0$ as apices. | |
| Apr 3, 2022 at 17:20 | comment | added | user332905 | @SamHopkins Can you give an example of a cone with more than one apex? | |
| Apr 3, 2022 at 17:16 | comment | added | Sam Hopkins | $C-a$ means the set $C-a := \{c-a\colon c\in C\}$ (this is like Minkowski sum notation). According to this definition, an example of a cone would be the open positive orthant $\{(x,y)\colon x, y >0\}$ in $\mathbb{R}^2$, which has apex the origin $(0,0)$, but the origin is not in the cone. | |
| Apr 3, 2022 at 17:09 | history | asked | user332905 | CC BY-SA 4.0 |