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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 ...
A finitary or n-ary relation is a set of n-tuples. Specific types of relations include: Relation (mathematics) (an elementary treatment of binary relations) Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation; Homogeneous relation; Reflexive relation; Serial relation
Relation, tuple, and attribute represented as table, row, and column respectively. In database theory, a relation, as originally defined by E. F. Codd, [1] is a set of tuples (d 1,d 2,...,d n), where each element d j is a member of D j, a data domain.
The next definition defines relation that formalizes the contents of a table as it is defined in the relational model. Relation A relation is a tuple (,) with , the header, and , the body, a set of tuples that all have the domain .
Relations with an adicity of two are called dyadic or binary. [13] Triadic or ternary relations have an adicity of three, like the relation of giving, which involves a giver, a receiver, and a given object. The relation of being between is also triadic since it requires two entities on the sides and one in the middle, as in "5 is between 2 and ...
In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution.. More precisely, if , …, are elements of a (left) module M over a ring R (the case of a vector space over a field is a special case), a relation between , …, is a sequence (, …,) of elements of R such that
Let be the set of ordered pairs of integers (,) with non-zero , and define an equivalence relation on such that (,) (,) if and only if =, then the equivalence class of the pair (,) can be identified with the rational number /, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of ...
The equality equivalence relation is the finest equivalence relation on any set, while the universal relation, which relates all pairs of elements, is the coarsest. The relation " ∼ {\displaystyle \sim } is finer than ≈ {\displaystyle \approx } " on the collection of all equivalence relations on a fixed set is itself a partial order ...