Ads
related to: order relation math examples problems
Search results
Results from the WOW.Com Content Network
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". This article introduces the field and provides basic definitions.
In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
Standard examples of posets arising in mathematics include: The real numbers, or in general any totally ordered set, ordered by the standard less-than-or-equal relation ≤, is a partial order. On the real numbers , the usual less than relation < is a strict partial order.
Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing a framework for saying when one thing is "less than" or "precedes" another. An alphabetical list of many notions of order theory can be found in the order theory glossary.
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} :
In Political science and Decision theory, order relations are typically used in the context of an agent's choice, for example the preferences of a voter over several political candidates. x ≺ y means that the voter prefers candidate y over candidate x. x ~ y means the voter is indifferent between candidates x and y.
In mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are immediate neighbours. The covering relation is commonly used to graphically express the partial order by means of the Hasse diagram .
A strict weak order that is trichotomous is called a strict total order. [14] The total preorder which is the inverse of its complement is in this case a total order. For a strict weak order < another associated reflexive relation is its reflexive closure, a (non-strict) partial order .
Ads
related to: order relation math examples problems