Binary relation and Indicator function

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Difference between Binary relation and Indicator function

Binary relation vs. Indicator function

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2. In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.

Complement (set theory)

In set theory, the complement of a set refers to elements not in.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Equality (mathematics)

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Order theory

Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.

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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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Power set

In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.

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Range (mathematics)

In mathematics, and more specifically in naive set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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Surjective function

In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).

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