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...
30 KB (4,360 words) - 19:22, 2 February 2024
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...
12 KB (1,882 words) - 01:42, 10 June 2024
Partially ordered set (redirect from Partial ordering relation)
contained in some total order. Stochastic dominance – Partial order between random variables Strict weak ordering – strict partial order "<" in which the relation...
40 KB (5,391 words) - 07:42, 25 August 2024
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...
21 KB (3,094 words) - 17:19, 9 April 2024
Consistency model (section Weak ordering)
therefore no additional safety net is required for weak ordering. In order to maintain weak ordering, write operations prior to a synchronization operation...
57 KB (7,630 words) - 21:16, 28 July 2024
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...
881 bytes (129 words) - 23:11, 21 July 2024
to weak ordering. They must label synchronization accesses as acquires or releases, not just as synchronization accesses. Similar to weak ordering, Release...
11 KB (1,358 words) - 10:01, 6 November 2023
Monotonic function (redirect from Weakly increasing)
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...
19 KB (2,467 words) - 04:06, 27 August 2024
Kruskal's tree theorem (category Order theory)
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...
14 KB (1,739 words) - 03:21, 29 July 2024
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...
37 KB (5,047 words) - 08:20, 12 May 2024
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...
2 KB (243 words) - 16:23, 10 July 2021
such comparison operator or comparator function must guarantee strict weak ordering. Apart from these, algorithms are provided for making heap from a range...
24 KB (2,136 words) - 01:31, 6 April 2024
Preorder (redirect from Quasi-ordering)
} is an equivalence; in that case " < {\displaystyle <} " is a strict weak order. The resulting preorder is connected (formerly called total); that is...
23 KB (3,351 words) - 13:50, 21 July 2024
Ordered field (redirect from Field ordering)
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...
14 KB (2,208 words) - 10:00, 10 June 2024
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...
18 KB (3,049 words) - 11:59, 22 May 2024
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...
31 KB (4,508 words) - 03:55, 24 August 2024
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...
40 KB (5,663 words) - 17:53, 6 June 2024
consistent with reachability. This ordering on the weak components can alternatively be interpreted as a weak ordering on the vertices themselves, with...
11 KB (1,591 words) - 22:32, 9 March 2024
NYPD's Chief of Detectives which became a recurring part. The episodes "Weak", "Contagious" and "Identity" starred Mary Stuart Masterson as Dr. Rebecca...
50 KB (2,627 words) - 16:55, 19 August 2024
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...
802 bytes (150 words) - 19:28, 10 August 2021
other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections. Formally, given...
7 KB (997 words) - 20:41, 15 December 2022
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...
1 KB (181 words) - 23:10, 2 November 2022
Inversion (discrete mathematics) (redirect from Weak order of permutations)
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...
15 KB (1,903 words) - 03:11, 4 January 2024
symmetric preorder Strict weak ordering – a strict partial order in which incomparability is an equivalence relation Total ordering – a connected (total)...
17 KB (2,076 words) - 19:51, 22 July 2024
Semiorder (redirect from Semi-order)
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...
17 KB (2,281 words) - 19:12, 4 February 2024
Sorting (redirect from Ascending order)
Sorting refers to ordering data in an increasing or decreasing manner according to some linear relationship among the data items. ordering: arranging items...
6 KB (778 words) - 16:31, 19 May 2024
transitive, total, trichotomous, a partial order, total order, strict weak order, total preorder (weak order), or an equivalence relation, then so too...
63 KB (8,832 words) - 17:38, 7 September 2024
{\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...
5 KB (744 words) - 13:42, 24 March 2024
Hausdorff maximal principle (category Order theory)
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...
11 KB (2,001 words) - 07:21, 2 September 2024
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...
53 KB (6,381 words) - 04:47, 23 July 2024