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When it is desired to associate a numeric value with the result of a comparison between two data items, say a and b, the usual convention is to assign −1 if a < b, 0 if a = b and 1 if a > b. For example, the C function strcmp performs a three-way comparison and returns −1, 0, or 1 according to this convention, and qsort expects the ...
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 ...
An example of a binary relation is the "divides" relation over the set of prime numbers and the set of integers, in which each prime is related to each integer that is a multiple of , but not to an integer that is not a multiple of .
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
If X and Y are finite sets, then there exists a bijection between the two sets X and Y if and only if X and Y have the same number of elements. Indeed, in axiomatic set theory , this is taken as the definition of "same number of elements" ( equinumerosity ), and generalising this definition to infinite sets leads to the concept of cardinal ...
For example, the natural numbers with their standard order. A chain is a subset of a poset that is a totally ordered set. For example, {{}, {}, {,,}} is a chain. An antichain is a subset of a poset in which no two distinct elements are comparable.
Goat Cheese, Pecan, and Mixed Green Salad. This premade salad consists of mixed greens, pecans, dried cranberries, bell peppers, tomatoes, red onions, and goat cheese with a honey vinaigrette. The ...
The feasible regions of linear programming are defined by a set of inequalities. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1] It is used most often to compare two numbers on the number line by their size.