reflexive ordering
1ordering 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 …
2Strict 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… …
3Well-quasi-ordering — In mathematics, specifically order theory, a well quasi ordering or wqo is a well founded quasi ordering with an additional restriction on sequences that there is no infinite sequence x i with x i ot le x j for all i < j . Motivation We can use… …
4Partially 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,… …
5List of French in Action episodes — Leçon 1 Orientation= An introduction to French in Action: its creation, its components, and its functioning. How to work with the video programs and how to integrate them with the audio and print components. This is the only program in English;… …
6applied logic — Introduction the study of the practical art of right reasoning. The formalism (formal logic) and theoretical results of pure logic can be clothed with meanings derived from a variety of sources within philosophy as well as from other… …
7Order theory — For a topical guide to this subject, see Outline of order theory. Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as… …
8set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …
9Robertson–Seymour theorem — In graph theory, the Robertson–Seymour theorem (also called the graph minor theorem[1]) states that the undirected graphs, partially ordered by the graph minor relationship, form a well quasi ordering.[2] Equivalently, every family of graphs that …
10Well-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… …
