Talk:Cantor's first set theory article/Archive 1: Difference between revisions

Revision as of 19:47, 8 September 2007

Revision as of 00:40, 30 November 2007

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* Additionally, the partition definition only makes sense if the element c is greater than or EQUAL to every element in A and less than or EQUAL TO every element in B. If c is not included in A or B, then (A,B) cannot be a partition of R. --[[User:TedPavlic|TedPavlic]] 21:04, 7 March 2007 (UTC)

**The text seems fine, it does not say that c is greater than every element in A and less than every element in B.--[[User:Patrick|Patrick]] 11:23, 7 June 2007 (UTC)

***I you don't allow for "or equal to" in at least one place i'ts impossible to find such a partition. (Present a counterexample please in case I'm wrong.)[[User:YohanN7|YohanN7]] ([[User talk:YohanN7|talk]]) 00:40, 30 November 2007 (UTC)

* Note: the term "gapless" may be better than "complete". --[[User:TedPavlic|TedPavlic]] 21:17, 7 March 2007 (UTC)

:Complete is the correct word. From the article you linked: "In order theory and related fields such as lattice and ___domain theory, completeness generally refers to the existence of certain suprema or infima of some partially ordered set. Notable special usages of the term include the concepts of complete Boolean algebra, complete lattice, and complete partial order (cpo). Furthermore, an ordered field is complete if every non-empty subset of it that has an upper bound within the field has a least upper bound within the field, which should be compared to the (slightly different) order-theoretical notion of bounded completeness. Up to isomorphism there is only one complete ordered field: the field of real numbers (but note that this complete ordered field, which is also a lattice, is not a complete lattice)." [[User:Ossi|Ossi]] 19:45, 8 September 2007 (UTC)