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# Complement (set theory)

In set theory, the complement of a set refers to elements not in. [1]

60 relations: Algebra of sets, Backslash, Bayes' theorem, C++, Clojure, Common Lisp, Complement (set theory), Contraposition, De Morgan's laws, Element (mathematics), Elm (programming language), Falcon (programming language), GNU Octave, Haskell (programming language), Identity (mathematics), Integer, Involution (mathematics), Irrational number, Java (programming language), Julia (programming language), LaTeX, MATLAB, Modular arithmetic, Multiple (mathematics), Naive set theory, OCaml, PARI/GP, Partition of a set, Pascal (programming language), Perl, Perl 6, Pharo, PHP, Prolog, Python (programming language), R (programming language), Racket (programming language), Rational number, Real number, Ruby (programming language), Rust (programming language), Scala (programming language), Set (abstract data type), Set (mathematics), Set theory, Smalltalk, Springer Science+Business Media, SQL, Standard 52-card deck, Subset, ... Expand index (10 more) »

## Algebra of sets

The algebra of sets defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion.

## Backslash

The backslash (\) is a typographical mark (glyph) used mainly in computing and is the mirror image of the common slash (/).

## Bayes' theorem

In probability theory and statistics, Bayes’ theorem (alternatively Bayes’ law or Bayes' rule, also written as Bayes’s theorem) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

## C++

C++ ("see plus plus") is a general-purpose programming language.

## Clojure

Clojure (like "closure") is a dialect of the Lisp programming language.

## Common Lisp

Common Lisp (CL) is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 (R2004) (formerly X3.226-1994 (R1999)).

## Complement (set theory)

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

## Contraposition

In logic, contraposition is an inference that says that a conditional statement is logically equivalent to its contrapositive.

## De Morgan's laws

In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.

## Element (mathematics)

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

## Elm (programming language)

Elm is a domain-specific programming language for declaratively creating web browser-based graphical user interfaces.

## Falcon (programming language)

Falcon is an open source, multi-paradigm programming language.

## GNU Octave

GNU Octave is software featuring a high-level programming language, primarily intended for numerical computations.

Haskell is a standardized, general-purpose compiled purely functional programming language, with non-strict semantics and strong static typing.

## Identity (mathematics)

In mathematics an identity is an equality relation A.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

## Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

## Java (programming language)

Java is a general-purpose computer-programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.

## Julia (programming language)

Julia is a high-level dynamic programming language designed to address the needs of high-performance numerical analysis and computational science, without the typical need of separate compilation to be fast, while also being effective for general-purpose programming, web use or as a specification language.

## LaTeX

LaTeX (or; a shortening of Lamport TeX) is a document preparation system.

## MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

## Multiple (mathematics)

In science, a multiple is the product of any quantity and an integer.

## Naive set theory

Naïve set theory is any of several theories of sets used in the discussion of the foundations of mathematics.

## OCaml

OCaml, originally named Objective Caml, is the main implementation of the programming language Caml, created by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez and others in 1996.

## PARI/GP

PARI/GP is a computer algebra system with the main aim of facilitating number theory computations.

## Partition of a set

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

## Pascal (programming language)

Pascal is an imperative and procedural programming language, which Niklaus Wirth designed in 1968–69 and published in 1970, as a small, efficient language intended to encourage good programming practices using structured programming and data structuring. It is named in honor of the French mathematician, philosopher and physicist Blaise Pascal. Pascal was developed on the pattern of the ALGOL 60 language. Wirth had already developed several improvements to this language as part of the ALGOL X proposals, but these were not accepted and Pascal was developed separately and released in 1970. A derivative known as Object Pascal designed for object-oriented programming was developed in 1985; this was used by Apple Computer and Borland in the late 1980s and later developed into Delphi on the Microsoft Windows platform. Extensions to the Pascal concepts led to the Pascal-like languages Modula-2 and Oberon.

## Perl

Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages, Perl 5 and Perl 6.

## Perl 6

Perl 6 is a member of the Perl family of programming languages.

## Pharo

Pharo is an open source dynamic and reflective language inspired from the programming language and environment Smalltalk.

## PHP

PHP: Hypertext Preprocessor (or simply PHP) is a server-side scripting language designed for Web development, but also used as a general-purpose programming language.

## Prolog

Prolog is a general-purpose logic programming language associated with artificial intelligence and computational linguistics.

## Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

## R (programming language)

R is a programming language and free software environment for statistical computing and graphics that is supported by the R Foundation for Statistical Computing.

## Racket (programming language)

Racket (formerly PLT Scheme) is a general-purpose, multi-paradigm programming language in the Lisp-Scheme family.

## Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

## Real number

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

## Ruby (programming language)

Ruby is a dynamic, interpreted, reflective, object-oriented, general-purpose programming language.

## Rust (programming language)

Rust is a systems programming language sponsored by Mozilla which describes it as a "safe, concurrent, practical language," supporting functional and imperative-procedural paradigms.

## Scala (programming language)

Scala is a general-purpose programming language providing support for functional programming and a strong static type system.

## Set (abstract data type)

In computer science, a set is an abstract data type that can store unique values, without any particular order.

## 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 a branch of mathematical logic that studies sets, which informally are collections of objects.

## Smalltalk

Smalltalk is an object-oriented, dynamically typed, reflective programming language.

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

## SQL

SQL (S-Q-L, "sequel"; Structured Query Language) is a domain-specific language used in programming and designed for managing data held in a relational database management system (RDBMS), or for stream processing in a relational data stream management system (RDSMS).

## Standard 52-card deck

A deck of French playing cards is the most common deck of playing cards used today.

## 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.

## Symmetric difference

In mathematics, the symmetric difference, also known as the disjunctive union, of two sets is the set of elements which are in either of the sets and not in their intersection.

## Union (set theory)

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

## Universe (mathematics)

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation.

## Unix shell

A Unix shell is a command-line interpreter or shell that provides a traditional Unix-like command line user interface.

## Wolfram Mathematica

Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.

## World Wide Web Consortium

The World Wide Web Consortium (W3C) is the main international standards organization for the World Wide Web (abbreviated WWW or W3).

## XPath 2.0

XPath 2.0 is a version of the XPath language defined by the World Wide Web Consortium, W3C.

## XQuery

XQuery (XML Query) is a query and functional programming language that queries and transforms collections of structured and unstructured data, usually in the form of XML, text and with vendor-specific extensions for other data formats (JSON, binary, etc.). The language is developed by the XML Query working group of the W3C.

## Z shell

The Z shell (Zsh) is a Unix shell that can be used as an interactive login shell and as a command interpreter for shell scripting.

## .NET Framework

.NET Framework (pronounced dot net) is a software framework developed by Microsoft that runs primarily on Microsoft Windows.

## References

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