Search results
Results from the WOW.Com Content Network
In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies the following for all a , b {\displaystyle a,b} and c {\displaystyle c} in X {\displaystyle X} :
A relation that is functional and total. For example, the red and green relations in the diagram are functions, but the blue and black ones are not. An injection [d] A function that is injective. For example, the green relation in the diagram is an injection, but the red, blue and black ones are not. A surjection [d] A function that is surjective.
Total order. A total order T is a partial order in which, for each x and y in T, we have x ≤ y or y ≤ x. Total orders are also called linear orders or chains. Total relation. Synonym for Connected relation. Transitive relation. A relation R on a set X is transitive, if x R y and y R z imply x R z, for all elements x, y, z in X. Transitive ...
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that".
The definition of total order appeared first historically and is a first-order axiomatization of the ordering as a binary predicate. Artin and Schreier gave the definition in terms of positive cone in 1926, which axiomatizes the subcollection of nonnegative elements.
The search engine that helps you find exactly what you're looking for. Find the most relevant information, video, images, and answers from all across the Web.
A partial order is, by definition, a reflexive, transitive and antisymmetric relation. A total order is a partial order that is connex. A relation R {\displaystyle R} is contained in another relation S {\displaystyle S} when all ordered pairs in R {\displaystyle R} also appear in S ; {\displaystyle S;} that is, x R y {\displaystyle xRy} implies ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!