657,269
edits
No edit summary |
m (Text replacement - "t''' " to "t</B> ") |
||
Line 22: | Line 22: | ||
=== 2014 === | === 2014 === | ||
* (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/partially_ordered_set Retrieved:2014-9-17. | * (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/partially_ordered_set Retrieved:2014-9-17. | ||
** In [[mathematics]], especially [[order theory]], a '''partially ordered set | ** In [[mathematics]], especially [[order theory]], a '''partially ordered set</B> (or '''poset''') formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a [[Set (mathematics)|set]]. A poset consists of a set together with a [[Relation (mathematics)|binary relation]] that indicates that, for certain pairs of elements in the set, one of the elements precedes the other. Such a relation is called a ''partial order'' to reflect the fact that not every pair of elements need be related: for some pairs, it may be that neither element precedes the other in the poset. <P> Thus, partial orders generalize the more familiar [[total order]]s, in which every pair is related. A finite poset can be visualized through its [[Hasse diagram]], which depicts the ordering relation. <P> A '''familiar''' real-life example of a partially ordered set is a collection of people ordered by [[genealogy|genealogical]] descendancy. Some pairs of people bear the descendant-ancestor relationship, but other pairs bear no such relationship. | ||
===2009=== | ===2009=== |