Idempotence and Lattice (order)

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Difference between Idempotence and Lattice (order)

Idempotence vs. Lattice (order)

Idempotence is the property of certain operations in mathematics and computer science that they can be applied multiple times without changing the result beyond the initial application. A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

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Binary operation

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Closure operator

In mathematics, a closure operator on a set S is a function \operatorname: \mathcal(S)\rightarrow \mathcal(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y\subseteq S |- | X \subseteq \operatorname(X) | (cl is extensive) |- | X\subseteq Y \Rightarrow \operatorname(X) \subseteq \operatorname(Y) | (cl is increasing) |- | \operatorname(\operatorname(X)).

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Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

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Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

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Join and meet

In a partially ordered set P, the join and meet of a subset S are respectively the supremum (least upper bound) of S, denoted ⋁S, and infimum (greatest lower bound) of S, denoted ⋀S.

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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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Module (mathematics)

In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.

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Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

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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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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

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Union (set theory)

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

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