In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose...

every non-empty subset of S has a least element in this ordering. The set S together with the ordering is then called a well-ordered set. In some academic...

contained in some total order. Stochastic dominance – Partial order between random variables Strict weak ordering – strict partial order "<" in which the relation...

ordered set then f induces a total ordering on X by setting x1 ≤ x2 if and only if f(x1) ≤ f(x2). The lexicographical order on the Cartesian product of a family...

therefore no additional safety net is required for weak ordering. In order to maintain weak ordering, write operations prior to a synchronization operation...

up weak in Wiktionary, the free dictionary. Weak may refer to: "Weak" (AJR song), 2016 "Weak" (Melanie C song), 2011 "Weak" (SWV song), 1993 "Weak" (Skunk...

to weak ordering. They must label synchronization accesses as acquires or releases, not just as synchronization accesses. Similar to weak ordering, Release...

f\!\left(y\right)} .) To avoid ambiguity, the terms weakly monotone, weakly increasing and weakly decreasing are often used to refer to non-strict monotonicity...

variants of the theorem can be expressed in subsystems of second-order arithmetic much weaker than the subsystems where they can be proved. This was first...

nonempty subsets. A weak ordering may be obtained from such a partition by choosing one of k ! {\displaystyle k!} total orderings of its subsets. Therefore...

processes can observe only one consistent state. The original paper on weak ordering: M. Dubois, C. Scheurich and F. A. Briggs, Memory Access Buffering in...

such comparison operator or comparator function must guarantee strict weak ordering. Apart from these, algorithms are provided for making heap from a range...

its standard ordering (which is also its only ordering); the field R {\displaystyle \mathbb {R} } of real numbers with its standard ordering (which is also...

} is an equivalence; in that case " < {\displaystyle <} " is a strict weak order. The resulting preorder is connected (formerly called total); that is...

In mathematics, specifically order theory, a well-quasi-ordering or wqo on a set X {\displaystyle X} is a quasi-ordering of X {\displaystyle X} for which...

and relations of a partial ordering. These are graph drawings where the vertices are the elements of the poset and the ordering relation is indicated by...

NYPD's Chief of Detectives which became a recurring part. The episodes "Weak", "Contagious" and "Identity" starred Mary Stuart Masterson as Dr. Rebecca...

consistent with reachability. This ordering on the weak components can alternatively be interpreted as a weak ordering on the vertices themselves, with...

the lattice of normal subgroups of a group. The set of first-order terms with the ordering "is more specific than" is a non-modular lattice used in automated...

refer to orderings that describe human preferences for one thing over an other. In mathematics, preferences may be modeled as a weak ordering or a semiorder...

other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections. Formally, given...

specifically in order theory and functional analysis, an element x {\displaystyle x} of a vector lattice X {\displaystyle X} is called a weak order unit in X...

as lex order by r {\displaystyle r} . The set of permutations on n items can be given the structure of a partial order, called the weak order of permutations...

symmetric preorder Strict weak ordering – a strict partial order in which incomparability is an equivalence relation Total ordering – a connected (total)...

In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are...

Sorting refers to ordering data in an increasing or decreasing manner according to some linear relationship among the data items. ordering: arranging items...

transitive, total, trichotomous, a partial order, total order, strict weak order, total preorder (weak order), or an equivalence relation, then so too...

{\displaystyle \mathbb {Z} [x]} is dense. On the other hand, the linear ordering on the integers is not dense. Georg Cantor proved that every two non-empty...

define (x0, y0) < (x1, y1) if y0 = y1 and x0 < x1. This is a partial ordering of R 2 {\displaystyle \mathbb {R} ^{2}} under which two points are comparable...

circular ordering (Mosher 1996, p. 109). Some authors call such an ordering a total cyclic order (Isli & Cohn 1998, p. 643), a complete cyclic order (Novák...