Talk:Order theory
Add topic| This is the talk page for discussing improvements to the Order theory article. This is not a forum for general discussion of the subject of the article. |
Article policies
|
Archives (index): 1Auto-archiving period: 2 years  |
 | This  level-5 vital article is rated C-class on Wikipedia's content assessment scale.It is of interest to the following WikiProjects: | ||||||||||
| |||||||||||
 | Text or other creative content from this version of Partial order was copied or moved into Order theory with this edit on March 13, 2004. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
 | Order theory was one of the Mathematics good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake. | ||||||||||||
| |||||||||||||
| Current status: Delisted good article | |||||||||||||
"<" or ">" as Order relations
[edit]Why are "≤" or "≥" used in the article's definition(s)? Regarding two 2 ordered things, one is less than the other, or vice versa. And it's nonsense to ask if something is less or more than itself. — Preceding unsigned comment added by 108.41.98.105 (talk) 19:06, 4 January 2023 (UTC)
- For total orders, it doesn't make a lot of difference which of these one uses. It is traditional to use ≤ for partial orders and < for (strict) weak orders; I don't know why. But for preorders, the = part of the ≤ relation is not equality, so in that case it is necessary to use ≤, to distinguish the case of two distinct elements that are both ≤ each other from the case of two incomparable elements. —David Eppstein (talk) 19:23, 4 January 2023 (UTC)
Existence of incomparable elements in partial orders.
[edit]In the "Background and motivation" section it is written that "Those orders like the "subset-of" relation for which there exist incomparable elements are called partial orders; orders for which every pair of elements is comparable are total orders".
But since total orders are a type of partial orders, stating that "[...] relation for which there exist incomparable elements are called partial orders" is wrong. It should better be "[...] relation for which there may exist incomparable elements are called partial orders" Tribisector (talk) 06:59, 8 December 2025 (UTC)
- I would replace "for which there exist" by "which allow". —David Eppstein (talk) 08:16, 8 December 2025 (UTC)
- @David Eppstein so I should edit it? Tribisector (talk) 08:41, 8 December 2025 (UTC)
- Sounds like a good change to me. Go for it. Stepwise Continuous Dysfunction (talk) 20:54, 8 December 2025 (UTC)
- @David Eppstein so I should edit it? Tribisector (talk) 08:41, 8 December 2025 (UTC)