Definitions for partially ordered set
par·tial·ly or·dered set

WiktionaryRate this definition:0.0 / 0 votes

1. partially ordered setnoun

   A set having a specified partial order.

2. partially ordered setnoun

   Said set together with said partial order; the ordered pair of said set and said partial order.

WikipediaRate this definition:0.0 / 0 votes

1. Partially ordered set

   In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order." The word partial in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable.

WikidataRate this definition:0.0 / 0 votes

1. Partially ordered set

   In mathematics, especially order theory, a partially ordered set formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a 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. Thus, partial orders generalize the more familiar total orders, in which every pair is related. A finite poset can be visualized through its Hasse diagram, which depicts the ordering relation. A familiar real-life example of a partially ordered set is a collection of people ordered by genealogical descendancy. Some pairs of people bear the descendant-ancestor relationship, but other pairs bear no such relationship. Another real-life example is the set of all street addresses in a town: 50 Maple St. is clearly "before" 52 Maple St. and "after" 48 Maple St., therefore all Maple St. addresses are ordered. Also, all Pine St. addresses are ordered in the same way. But you cannot tell if 50 Maple St. is "before" or "after" 300 Pine St. in this way, so any set that includes addresses on both streets is only partially ordered. The set of Maple St. addresses alone is a totally ordered set.

How to pronounce partially ordered set?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say partially ordered set in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of partially ordered set in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of partially ordered set in Pythagorean Numerology is: 2

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Partially_Ordered_Set
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Partially_Ordered_Set
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=partially ordered set