Timeline for How two elements relate in this poset?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22, 2017 at 19:39 | history | edited | Santana Afton | CC BY-SA 3.0 | clarification of a mistake I made |
| Mar 21, 2017 at 15:01 | comment | added | CiaPan | There is no largest element in a described order, unless $S$ is empty (in which case the empty function is the only candidate) or $T$ is a singleton (in which case the largest element is a function whose domain is whole $S$). | |
| Mar 21, 2017 at 13:02 | comment | added | Zed | Yeah, but that's not the only condition, like if we take all functions greater than f and g the least upper bound is the function that is relates to both f and g but it's immediately above it (if we looked at the hassle diagram of the relation) | |
| Mar 21, 2017 at 12:58 | comment | added | Santana Afton | By greatest lower bound, do you mean the greatest function which is less than both $f$ and $g$? | |
| Mar 21, 2017 at 12:53 | comment | added | Zed | For the example you wrote it is the case iff your function was 1/x, otherwise the greatest element is the element that maps the whole source set, right? Also the greatest lower bound of f and g will be defined by the intersection of Dom(f) and Dom(g), and for the least upper bound it will be defined by their union of the domains, does that sound right? Thanks. | |
| Mar 21, 2017 at 12:37 | comment | added | Santana Afton | That's a good point that I overlooked, thank you! I edited my response to reflect the change. | |
| Mar 21, 2017 at 12:36 | history | edited | Santana Afton | CC BY-SA 3.0 | Fixed error in argument. |
| Mar 21, 2017 at 12:06 | comment | added | Zed | I understood the relation now thanks, the minimal and maximal elements are also the least and the greatest since they are the only minimal and maximal, right? Thanks | |
| Mar 21, 2017 at 10:47 | history | answered | Santana Afton | CC BY-SA 3.0 |