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

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**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)
* 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)
 
The article linked to complete lattices, and you're right the reals are not a complete lattice. They are a complete metric space, but that is not the subject here. I reworded it a little. I don't think "gapless" is better - we should try to explain things, but not to the point of inventing our own terminology. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 13:15, 23 July 2007 (UTC)