Talk:Preorder

From Wikipedia, the free encyclopedia

[edit] Types of preorders

Is there a commonly-used name for a complete preorder (sequence A000670 in OEIS) within set theory? (Not a total order, mind you -- it need not be antisymmetric.) I've heard the term "weak order", but that's from the same field that uses "linear order" for total orders, so I wanted some clarification if anyone knows of something else. CRGreathouse (t | c) 20:02, 30 August 2006 (UTC)

Total preorders, of course. Thanks, Hurkyl! CRGreathouse (t | c) 04:55, 31 August 2006 (UTC)

[edit] Table

The table which shows the number of preorders needs some explanation. What precisely does the value n (given for n=1,2,3,4) denote? —Preceding unsigned comment added by 66.108.155.231 (talk) 02:19, August 28, 2007 (UTC)

That's the number of elements to be preordered. If there's just one element there's only one preorder (a <~ a). If there are two elements there are four preorders: (a <~ a, b <~ b, a <~ b), (a <~ a, b <~ b, b <~ a), (a <~ a, b <~ b, a <~ b, b <~ a), (a <~ a, b <~ b). CRGreathouse (t | c) 16:11, 4 October 2007 (UTC)