partial ordering

par·tial or·der

P p

Definitions of partial ordering words

noun partial ordering a relation defined on a set, having the properties that each element is in relation to itself, the relation is transitive, and if two elements are in relation to each other, the two elements are equal. 1
noun Definition of partial ordering in Technology A relation R is a partial ordering if it is a pre-order (i.e. it is reflexive (x R x) and transitive (x R y R z => x R z)) and it is also antisymmetric (x R y R x => x = y). The ordering is partial, rather than total, because there may exist elements x and y for which neither x R y nor y R x. In domain theory, if D is a set of values including the undefined value (bottom) then we can define a partial ordering relation <= on D by x <= y if x = bottom or x = y. The constructed set D x D contains the very undefined element, (bottom, bottom) and the not so undefined elements, (x, bottom) and (bottom, x). The partial ordering on D x D is then (x1,y1) <= (x2,y2) if x1 <= x2 and y1 <= y2. The partial ordering on D -> D is defined by f <= g if f(x) <= g(x) for all x in D. (No f x is more defined than g x.) A lattice is a partial ordering where all finite subsets have a least upper bound and a greatest lower bound. ("<=" is written in LaTeX as \sqsubseteq). 1
noun partial ordering an ordering that is reflexive, antisymmetric, and transitive, as set inclusion 0

before 1940

One of the 7% newest English words

First recorded in 1940-45

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This term is known only to a narrow circle of people with rare knowledge. Only 5% of English native speakers know the meaning of this word.

According to our data most of word are more popular. This word is almost not used. It has a much more popular synonym.

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