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# Tuple

A tuple is a finite ordered list of elements. [1]

## Abraham Fraenkel

Abraham Halevi (Adolf) Fraenkel (אברהם הלוי (אדולף) פרנקל; February 17, 1891, Munich, Germany – October 15, 1965, Jerusalem, Israel), known as Abraham Fraenkel, was a German-born Israeli mathematician.

## Arity

In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands the function or operation accepts.

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## Azriel Lévy

Azriel Lévy (Hebrew: עזריאל לוי; born c. 1934) is an Israeli mathematician, logician, and a professor emeritus at the Hebrew University of Jerusalem.

## Binary relation

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

## Cardinality

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

## Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers and is the imaginary unit, that satisfies the equation.

## Discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

## Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

## Exponential object

In mathematics, specifically in category theory, an exponential object is the categorical equivalent of a function space in set theory.

## Formal language

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols that may be constrained by rules that are specific to it.

## Functional programming

In computer science, functional programming is a programming paradigm—a style of building the structure and elements of computer programs—that treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data.

## Gaisi Takeuti

is a Japanese mathematician, known for his work in proof theory.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## Keith Devlin

Keith J. Devlin is a British mathematician and popular science writer.

## Latin

Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

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## Linguistics

Linguistics is the scientific study of language.

## Mathematics

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

## Model theory

In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.

## Multiset

In mathematics, a multiset (or bag) is a generalization of the concept of a set that, unlike a set, allows multiple instances of the multiset's elements.

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## Octonion

In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are only four such algebras, the other three being the real numbers R, the complex numbers C, and the quaternions H. The octonions are the largest such algebra, with eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.

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## Ordered pair

In mathematics, an ordered pair (a, b) is a pair of mathematical objects.

## Philosophy

Philosophy is the study of the general and fundamental nature of reality, existence, knowledge, values, reason, mind, and language.

## Preprint

In academic publishing, a preprint is a draft of a scientific paper that has not yet been published in a peer-reviewed scientific journal.

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## Prime k-tuple

In number theory, a prime k-tuple is a finite collection of values representing a repeatable pattern of differences between prime numbers.

## Probability theory

Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena.

## Product type

In programming languages and type theory, a product of types is another, compounded, type in a structure.

## Programming language

A programming language is a formal constructed language designed to communicate instructions to a machine, particularly a computer.

## Projection (mathematics)

In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent).

## Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

## Record (computer science)

In computer science, a record (also called struct or compound data) is a basic data structure (a tuple may or may not be considered a record, and vice versa, depending on conventions and the programming language at hand).

## Recursive definition

A recursive definition (or inductive definition) in mathematical logic and computer science is used to define the elements in a set in terms of other elements in the set (Aczel 1978:740ff).

## Relational algebra

Relational algebra, first described by E.F. Codd while at IBM, is a family of algebra with a well-founded semantics used for modelling the data stored in relational databases, and defining queries on it.

## Resource Description Framework

The Resource Description Framework (RDF) is a family of World Wide Web Consortium (W3C) specifications originally designed as a metadata data model.

## Rule of product

In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting).

## Sedenion

In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals obtained by applying the Cayley–Dickson construction to the octonions.

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## Semantic Web

The Semantic Web is an extension of the Web through standards by the World Wide Web Consortium (W3C).

## Sequence

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

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## Set (mathematics)

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

## Set theory

Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects.

## Simply typed lambda calculus

The simply typed lambda calculus (\lambda^\to), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor: \to that builds function types.

## Singleton (mathematics)

In mathematics, a singleton, also known as a unit set, is a set with exactly one element.

## Tuple space

A tuple space is an implementation of the associative memory paradigm for parallel/distributed computing.

## Type theory

In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics.

## Unit type

In the area of mathematical logic and computer science known as type theory, a unit type is a type that allows only one value (and thus can hold no information).

## Vector (mathematics and physics)

When used without any further description, vector refers either to.

## Yehoshua Bar-Hillel

Yehoshua Bar-Hillel (יהושע בר-הלל; 8 September 1915, Vienna – 25 September 1975, Jerusalem) was an Israeli philosopher, mathematician, and linguist.

## References

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