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Iterated binary operation

Index Iterated binary operation

In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. [1]

30 relations: Addition, Associative property, Binary operation, Binary tree, Bird–Meertens formalism, Continued fraction, Exclusive or, Finite set, Fold (higher-order function), Function (mathematics), Hausdorff space, Identity element, Infinite product, Infinity, Intersection (set theory), Limit of a sequence, Logical conjunction, Magma (algebra), Mathematics, Metric (mathematics), Monoid, Multiplication, Multiset, Product (mathematics), Proposition, Sequence, Series (mathematics), Summation, Topology, Union (set theory).

Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

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Associative property

In mathematics, the associative property is a property of some binary operations.

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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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Binary tree

In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the and the.

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Bird–Meertens formalism

The Bird–Meertens formalism (BMF) is a calculus for deriving programs from specifications (in a functional-programming setting) by a process of equational reasoning.

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Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

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Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

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Finite set

In mathematics, a finite set is a set that has a finite number of elements.

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Fold (higher-order function)

In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.

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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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Hausdorff space

In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.

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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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Infinite product

In mathematics, for a sequence of complex numbers a1, a2, a3,...

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Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

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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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Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

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Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

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Magma (algebra)

In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure.

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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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Metric (mathematics)

In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.

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Monoid

In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.

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Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

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Multiset

In mathematics, a multiset (aka bag or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements.

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Product (mathematics)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.

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Proposition

The term proposition has a broad use in contemporary analytic philosophy.

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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

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Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

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Summation

In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.

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Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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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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References

[1] https://en.wikipedia.org/wiki/Iterated_binary_operation

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