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As a relation between some temporal events and some spatial events, hyperbolic orthogonality (as found in split-complex numbers) is a heterogeneous relation. [21] A geometric configuration can be considered a relation between its points and its lines. The relation is expressed as incidence. Finite and infinite projective and affine planes are ...
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.
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 ...
List of set identities and relations – Equalities for combinations of sets; Logical conjunction – Logical connective AND; MinHash – Data mining technique; Naive set theory – Informal set theories; Symmetric difference – Elements in exactly one of two sets; Union – Set of elements in any of some sets
A binary relation between sets A and B is a subset of A × B. The ( a , b ) notation may be used for other purposes, most notably as denoting open intervals on the real number line . In such situations, the context will usually make it clear which meaning is intended.
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 ...
The elementary operation of counting establishes a bijection from some finite set to the first natural numbers (1, 2, 3, ...), up to the number of elements in the counted set. It results that two finite sets have the same number of elements if and only if there exists a bijection between them. More generally, two sets are said to have the same ...
For a ≤ b, the closed interval [a, b] is the set of elements x satisfying a ≤ x ≤ b (that is, a ≤ x and x ≤ b). It contains at least the elements a and b. Using the corresponding strict relation "<", the open interval (a, b) is the set of elements x satisfying a < x < b (i.e. a < x and x < b). An open interval may be empty even if a < b.