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In mathematics, a relation on a set may, or may not, hold between two given members of the set. 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 values 3 and 1 nor between 4 ...
In mathematics, a finitary relation over a sequence of sets X 1, ..., X n is a subset of the Cartesian product X 1 × ... Definition R is an n-ary relation on sets X ...
Symbolic statement. In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c . Every partial order and every equivalence relation is transitive. For example, less than and equality among real numbers are both transitive: If a < b and b < c ...
A recurrence relation is an equation that expresses each element of a sequence as a function of the preceding ones. More precisely, in the case where only the immediately preceding element is involved, a recurrence relation has the form. where. is a function, where X is a set to which the elements of a sequence must belong.
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number is equal to itself (reflexive). If , then (symmetric).
Binary relation. In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. [1] Precisely, a binary relation over sets and is a set of ordered pairs consisting of elements from and from . [2]
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
Relational algebra is a branch of mathematics that studies the manipulation and analysis of data in relational databases. It defines a set of operations, such as selection, projection, join, and union, that can be applied to relations or sets of tuples. Learn more about the concepts and notation of relational algebra on Wikipedia, including the rename operation that changes the attribute name ...