Talk:Maximal and minimal elements

changes
Hello. Sorry about not communicating the reason for the changes. As a matter or fact, I did not erase anything in the article but rather reorganized it. For instance, the mention to a subset of a power set, before in a paragraph, is now example 5. I did add some clarifications as for the relations between maximal element and greatest element as well as section on preference preorders where maximal element means something different. Xurxo.duran 12:53, 2 March 2007 (UTC)

economics
Why does economics come in here. Should be a purely mathemetical definition. —Preceding unsigned comment added by 130.37.31.232 (talk) 12:48, 30 July 2009 (UTC)

Possible error?
The statement, "In set theory, a set is finite if and only if every non-empty family of subsets has a minimal element when ordered by the inclusion relation.", occurs in this article. I am wondering if it should be modified to say "Maximal" instead of "minimal;" The empty set is included in every family of sets, finite or not, and it is certainly a minimum set, if not a "minimal" set. Is the distinction between minimal and minimum in play here? To be clear, I am NOT presuming to make this edit; I am seeking clarification of the concept of minimal for my own understanding. I would very much appreciate a reply to my question; reply to . — Preceding unsigned comment added by 174.22.14.156 (talk) 00:26, 14 April 2016 (UTC)
 * But the empty set isn't included in every family of sets? (That is, the empty set need not be an element of a given family of sets. It is of course a subset of any family of sets.) – Tobias Bergemann (talk) 08:23, 14 April 2016 (UTC)
 * But you are right, the article could say "maximal" instead of "minimal". What the statement is trying to express is that a set is finite if and only if there are no infinite chains in its power set when ordered by inclusion. – Tobias Bergemann (talk) 08:27, 14 April 2016 (UTC)

Move discussion in progress
There is a move discussion in progress on Talk:Upper and lower bounds which affects this page. Please participate on that page and not in this talk page section. Thank you. —RMCD bot 20:14, 12 September 2017 (UTC)