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...

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...

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

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

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

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...

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

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...

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...

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

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...

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...

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...

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...

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...

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...

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

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

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

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...

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...

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...

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

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

Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing...

these topologies. McCord also showed that these spaces are weak homotopy equivalent to the order complex of the corresponding partially ordered set. Steiner...

is called orderable or linearly orderable if there exists a total order on its elements such that the order topology induced by that order and the given...