# total ordering relation

### Look at other dictionaries:

**ordering relation**— A partial ordering on a set is a relation < that is transitive and reflexive and antisymmetric. That is, (i) x < y & y < z →x < z ; (ii) x < x ; (iii) x < y & y < x →x = y . If we add (iv) that at least one of x < y, x = y … Philosophy dictionary**total order**— noun A relation that is reflexive, antisymmetric, and transitive (i.e., that is a partial order), and having the property that for any two elements of its set, one is related to the other. Syn: total ordering re … Wiktionary**Total order**— In set theory, a total order, linear order, simple order, or (non strict) ordering is a binary relation (here denoted by infix ≤) on some set X. The relation is transitive, antisymmetric, and total. A set paired with a total order is called a… … Wikipedia**Transitive relation**— In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b , and b is in turn related to an element c , then a is also related to c . Transitivity is a key property of both partial order… … Wikipedia**Binary relation**— Relation (mathematics) redirects here. For a more general notion of relation, see Finitary relation. For a more combinatorial viewpoint, see Theory of relations. In mathematics, a binary relation on a set A is a collection of ordered pairs of… … Wikipedia**Strict weak ordering**— The 13 possible strict weak orderings on a set of three elements {a, b, c}. The only partially ordered sets are coloured, while totally ordered ones are in black. Two orderings are shown as connected by an edge if they differ by a single… … Wikipedia**Well-founded relation**— In mathematics, a binary relation, R, is well founded (or wellfounded) on a class X if and only if every non empty subset of X has a minimal element with respect to R; that is, for every non empty subset S of X, there is an element m of S such… … Wikipedia**Equivalence relation**— In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being equivalent in some way. Let a , b , and c be arbitrary elements of some set X . Then a b or a ≡ b denotes that a is… … Wikipedia**Belief revision**— is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents.What… … Wikipedia**Partially ordered set**— The Hasse diagram of the set of all subsets of a three element set {x, y, z}, ordered by inclusion. In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering,… … Wikipedia