Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!
And Ads-free!

Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first, literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch"). [1]

104 relations: Abelian group, Absolute value, Abstract algebra, Additive identity, Additive inverse, Aleph number, Algebraic expression, Algebraic integer, Algebraic number field, Algebraic number theory, Algebraic structure, ALGOL 68, Arbitrary-precision arithmetic, Associative property, −1, Bijection, Binary operation, Blackboard bold, C (programming language), Cardinality, Category of rings, Closure (mathematics), Commutative property, Commutative ring, Countable set, Cyclic group, Data type, Discrete valuation ring, Distributive property, Division (mathematics), Embedding, Emphasis (typography), Equality (mathematics), Equivalence class, Equivalence relation, Eric Temple Bell, Euclidean algorithm, Euclidean division, Euclidean domain, Exponentiation, Field (mathematics), Field of fractions, Floor and ceiling functions, Fraction (mathematics), French language, Fundamental theorem of arithmetic, Garrett Birkhoff, German language, Greatest common divisor, Group (mathematics), ..., Group isomorphism, Group representation, Hyperinteger, Identity element, If and only if, Initial and terminal objects, Injective function, Integer lattice, Integer sequence, Integer-valued function, Integral domain, Inverse element, Java (programming language), Latin, List of mathematical symbols, Men of Mathematics, Monoid, Multiplication, Natural number, Noetherian ring, Number, Object Pascal, On-Line Encyclopedia of Integer Sequences, Ordered pair, Ordered ring, Prime number, Principal ideal domain, Profinite integer, Programming language, Rational number, Real number, Remainder, Ring (mathematics), Ring homomorphism, Ring of integers, Saunders Mac Lane, Set (mathematics), Sign (mathematics), Subring, Subset, Subtraction, Surjective function, Total order, Two's complement, Unicode, Universal property, Universal quantification, Valuation ring, Well-order, Wolfram Demonstrations Project, Zero divisor, 0 (number), 0.999..., 1 (number). Expand index (54 more) »

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written (the axiom of commutativity).

New!!: Integer and Abelian group · See more »

Absolute value

In mathematics, the absolute value (or modulus) of a real number is the non-negative value of without regard to its sign.

New!!: Integer and Absolute value · See more »

Abstract algebra

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

New!!: Integer and Abstract algebra · See more »

Additive identity

In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.

New!!: Integer and Additive identity · See more »

Additive inverse

In mathematics, the additive inverse of a number is the number that, when added to, yields zero.

New!!: Integer and Additive inverse · See more »

Aleph number

In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.

New!!: Integer and Aleph number · See more »

Algebraic expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

New!!: Integer and Algebraic expression · See more »

Algebraic integer

In number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in (the set of integers).

New!!: Integer and Algebraic integer · See more »

Algebraic number field

In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.

New!!: Integer and Algebraic number field · See more »

Algebraic number theory

Algebraic number theory is a major branch of number theory that studies algebraic structures related to algebraic integers.

New!!: Integer and Algebraic number theory · See more »

Algebraic structure

In mathematics, and more specifically in abstract algebra, the term algebraic structure generally refers to a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a some list of axioms.

New!!: Integer and Algebraic structure · See more »

ALGOL 68

ALGOL 68 (short for ALGOrithmic Language 1968) is an imperative computer programming language that was conceived as a successor to the ALGOL 60 programming language, designed with the goal of a much wider scope of application and more rigorously defined syntax and semantics.

New!!: Integer and ALGOL 68 · See more »

Arbitrary-precision arithmetic

In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system.

New!!: Integer and Arbitrary-precision arithmetic · See more »

Associative property

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

New!!: Integer and Associative property · See more »

−1

In mathematics, −1 is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0.

New!!: Integer and −1 · See more »

Bijection

In mathematics, a bijection, bijective function or one-to-one correspondence is a function between the elements of two sets, where every element of one set is paired with exactly one element of the other set, and every element of the other set is paired with exactly one element of the first set.

New!!: Integer and Bijection · See more »

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 (more formally, an operation whose arity is two, and whose two domains and one codomain are (subsets of) the same set).

New!!: Integer and Binary operation · See more »

Blackboard bold

Blackboard bold is a typeface style that is often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical or near-vertical lines) are doubled.

New!!: Integer and Blackboard bold · See more »

C (programming language)

C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.

New!!: Integer and C (programming language) · See more »

Cardinality

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

New!!: Integer and Cardinality · See more »

Category of rings

In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (preserving the identity).

New!!: Integer and Category of rings · See more »

Closure (mathematics)

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.

New!!: Integer and Closure (mathematics) · See more »

Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

New!!: Integer and Commutative property · See more »

Commutative ring

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

New!!: Integer and Commutative ring · See more »

Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

New!!: Integer and Countable set · See more »

Cyclic group

In algebra, a cyclic group is a group that is generated by a single element.

New!!: Integer and Cyclic group · See more »

Data type

In computer science and computer programming, a data type or simply type is a classification identifying one of various types of data, such as real, integer or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of that type can be stored.

New!!: Integer and Data type · See more »

Discrete valuation ring

In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.

New!!: Integer and Discrete valuation ring · See more »

Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from elementary algebra.

New!!: Integer and Distributive property · See more »

Division (mathematics)

In mathematics, especially in elementary arithmetic, division (denoted ÷ or / or —) is an arithmetic operation.

New!!: Integer and Division (mathematics) · See more »

Embedding

In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.

New!!: Integer and Embedding · See more »

Emphasis (typography)

In typography, emphasis is the exaggeration of words in a text with a font in a different style from the rest of the text—to emphasize them.

New!!: Integer and Emphasis (typography) · See more »

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.

New!!: Integer and Equality (mathematics) · See more »

Equivalence class

In mathematics, when a set has an equivalence relation defined on its elements, there is a natural grouping of elements that are related to one another, forming what are called equivalence classes.

New!!: Integer and Equivalence class · See more »

Equivalence relation

In mathematics, an equivalence relation is the relation that holds between two elements if and only if they are members of the same cell within a set that has been partitioned into cells such that every element of the set is a member of one and only one cell of the partition.

New!!: Integer and Equivalence relation · See more »

Eric Temple Bell

Eric Temple Bell (February 7, 1883 – December 21, 1960) was a Scottish-born mathematician and science fiction writer who lived in the United States for most of his life.

New!!: Integer and Eric Temple Bell · See more »

Euclidean algorithm

. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.

New!!: Integer and Euclidean algorithm · See more »

Euclidean division

In arithmetic, the Euclidean division is the process of division of two integers, which produces a quotient and a remainder.

New!!: Integer and Euclidean division · See more »

Euclidean domain

In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain (also called a Euclidean ring) is a ring that can be endowed with a Euclidean function (explained below) which allows a suitable generalization of the Euclidean division of the integers.

New!!: Integer and Euclidean domain · See more »

Exponentiation

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: In that case, bn is called the n-th power of b, or b raised to the power n. The exponent is usually shown as a superscript to the right of the base.

New!!: Integer and Exponentiation · See more »

Field (mathematics)

In abstract algebra, a field is a nonzero commutative division ring, or equivalently a ring whose nonzero elements form an abelian group under multiplication.

New!!: Integer and Field (mathematics) · See more »

Field of fractions

In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded.

New!!: Integer and Field of fractions · See more »

Floor and ceiling functions

In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively.

New!!: Integer and Floor and ceiling functions · See more »

Fraction (mathematics)

A fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

New!!: Integer and Fraction (mathematics) · See more »

French language

French (le français or la langue française) is a Romance language, belonging to the Indo-European family.

New!!: Integer and French language · See more »

Fundamental theorem of arithmetic

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1Using the empty product rule one need not exclude the number 1, and the theorem can be stated as: every positive integer has unique prime factorization.

New!!: Integer and Fundamental theorem of arithmetic · See more »

Garrett Birkhoff

Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician.

New!!: Integer and Garrett Birkhoff · See more »

German language

German (Deutsch) is a West Germanic language that derives most of its vocabulary from the Germanic branch of the Indo-European language family.

New!!: Integer and German language · See more »

Greatest common divisor

In mathematics, the greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder.

New!!: Integer and Greatest common divisor · See more »

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements together with an operation that combines any two elements to form a third element.

New!!: Integer and Group (mathematics) · See more »

Group isomorphism

In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.

New!!: Integer and Group isomorphism · See more »

Group representation

In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.

New!!: Integer and Group representation · See more »

Hyperinteger

In non-standard analysis, a hyperinteger N is a hyperreal number equal to its own integer part.

New!!: Integer and Hyperinteger · See more »

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.

New!!: Integer and Identity element · See more »

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.

New!!: Integer and If and only if · See more »

Initial and terminal objects

In category theory, an abstract branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.

New!!: Integer and Initial and terminal objects · See more »

Injective function

In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.

New!!: Integer and Injective function · See more »

Integer lattice

In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted Zn, is the lattice in the Euclidean space Rn whose lattice points are ''n''-tuples of integers.

New!!: Integer and Integer lattice · See more »

Integer sequence

In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.

New!!: Integer and Integer sequence · See more »

Integer-valued function

In mathematics, an integer-valued function is a function whose values are integers.

New!!: Integer and Integer-valued function · See more »

Integral domain

In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.

New!!: Integer and Integral domain · See more »

Inverse element

In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.

New!!: Integer and Inverse element · See more »

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.

New!!: Integer and Java (programming language) · See more »

Latin

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

New!!: Integer and Latin · See more »

List of mathematical symbols

This is a list of symbols found within all branches of mathematics to express a formula or to represent a constant.

New!!: Integer and List of mathematical symbols · See more »

Men of Mathematics

Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincare is a book on the history of mathematics published in 1937 by Scottish-born American mathematician and science fiction writer E. T. Bell (1883-1960).

New!!: Integer and Men of Mathematics · See more »

Monoid

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

New!!: Integer and Monoid · See more »

Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "·" or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division.

New!!: Integer and Multiplication · See more »

Natural number

In mathematics, the natural numbers (sometimes called the whole numbers): "whole number An integer, though sometimes it is taken to mean only non-negative integers, or just the positive integers." give definitions of "whole number" under several headwords: INTEGER … Syn. whole number.

New!!: Integer and Natural number · See more »

Noetherian ring

In mathematics, more specifically in the area of abstract algebra known as ring theory, a Noetherian ring is a ring that satisfies the ascending chain condition on ideals; that is, given any chain: there exists an n such that: There are other equivalent formulations of the definition of a Noetherian ring and these are outlined later in the article.

New!!: Integer and Noetherian ring · See more »

Number

A number is a mathematical object used to count, measure and label.

New!!: Integer and Number · See more »

Object Pascal

Object Pascal refers to a branch of object-oriented derivatives of Pascal, mostly known as the primary programming language of Embarcadero Delphi.

New!!: Integer and Object Pascal · See more »

On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.

New!!: Integer and On-Line Encyclopedia of Integer Sequences · See more »

Ordered pair

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

New!!: Integer and Ordered pair · See more »

Ordered ring

In abstract algebra, an ordered ring is a (usually commutative) ring R with a total order ≤ such that for all a, b, and c in R.

New!!: Integer and Ordered ring · See more »

Prime number

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

New!!: Integer and Prime number · See more »

Principal ideal domain

In abstract algebra, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i.e., can be generated by a single element.

New!!: Integer and Principal ideal domain · See more »

Profinite integer

In mathematics, a profinite integer is an element of the ring where p runs over all prime numbers, \mathbb_p is the ring of ''p''-adic integers and \widehat.

New!!: Integer and Profinite integer · See more »

Programming language

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

New!!: Integer and Programming language · See more »

Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero.

New!!: Integer and Rational number · See more »

Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

New!!: Integer and Real number · See more »

Remainder

In mathematics, the remainder is the amount "left over" after performing some computation.

New!!: Integer and Remainder · See more »

Ring (mathematics)

In mathematics, and more specifically in algebra, a ring is an algebraic structure with operations that generalize the arithmetic operations of addition and multiplication.

New!!: Integer and Ring (mathematics) · See more »

Ring homomorphism

In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.

New!!: Integer and Ring homomorphism · See more »

Ring of integers

In mathematics, the ring of integers of an algebraic number field is the ring of all integral elements contained in.

New!!: Integer and Ring of integers · See more »

Saunders Mac Lane

Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.

New!!: Integer and Saunders Mac Lane · See more »

Set (mathematics)

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

New!!: Integer and Set (mathematics) · See more »

Sign (mathematics)

In mathematics, the concept of sign originates from the property of every non-zero real number to be positive or negative.

New!!: Integer and Sign (mathematics) · See more »

Subring

In mathematics, a subring of R is a subset of a ring that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and which shares the same multiplicative identity as R. For those who define rings without requiring the existence of a multiplicative identity, a subring of R is just a subset of R that is a ring for the operations of R (this does imply it contains the additive identity of R).

New!!: Integer and Subring · See more »

Subset

In mathematics, especially in set theory, 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.

New!!: Integer and Subset · See more »

Subtraction

Subtraction is a mathematical operation that represents the operation of removing objects from a collection.

New!!: Integer and Subtraction · See more »

Surjective function

In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if every element y in Y has a corresponding element x in X such that f(x).

New!!: Integer and Surjective function · See more »

Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ≤) on some set X which is transitive, antisymmetric, and total.

New!!: Integer and Total order · See more »

Two's complement

Two's complement is a mathematical operation on binary numbers, as well as a binary signed number representation based on this operation.

New!!: Integer and Two's complement · See more »

Unicode

Unicode is a computing industry standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems.

New!!: Integer and Unicode · See more »

Universal property

In various branches of mathematics, a useful construction is often viewed as the “most efficient solution” to a certain problem.

New!!: Integer and Universal property · See more »

Universal quantification

In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".

New!!: Integer and Universal quantification · See more »

Valuation ring

In abstract algebra, a valuation ring is an integral domain D such that for every element x of its field of fractions F, at least one of x or x −1 belongs to D. Given a field F, if D is a subring of F such that either x or x −1 belongs to D for every nonzero x in F, then D is said to be a valuation ring for the field F or a place of F. Since F in this case is indeed the field of fractions of D, a valuation ring for a field is a valuation ring.

New!!: Integer and Valuation ring · See more »

Well-order

In mathematics, a well-order relation (or well-ordering) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.

New!!: Integer and Well-order · See more »

Wolfram Demonstrations Project

The Wolfram Demonstrations Project is hosted by Wolfram Research, whose stated goal is to bring computational exploration to the widest possible audience.

New!!: Integer and Wolfram Demonstrations Project · See more »

Zero divisor

In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero such that, or equivalently if the map from to that sends to is not injective.

New!!: Integer and Zero divisor · See more »

0 (number)

0 (zero; BrE: or AmE) is both a number and the numerical digit used to represent that number in numerals.

New!!: Integer and 0 (number) · See more »

0.999...

In mathematics, the repeating decimal 0.999... (sometimes written with more or fewer 9s before the final ellipsis, for example as 0.9..., or in a variety of other variants such as 0.9, 0.(9), or) denotes a real number that can be shown to be the number ''one''.

New!!: Integer and 0.999... · See more »

1 (number)

1 (one; or, also called "unit", "unity", and "(multiplicative) identity", is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of "unit length" is a line segment of length 1.

New!!: Integer and 1 (number) · See more »

References

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

OutgoingIncoming
Hey! We are on Facebook now! »