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) » « Shrink index
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 ·
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 ·
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 ·
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 ·
In mathematics, the additive inverse of a number is the number that, when added to, yields zero.
New!!: Integer and Additive inverse ·
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 ·
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 ·
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 ·
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 ·
Algebraic number theory is a major branch of number theory that studies algebraic structures related to algebraic integers.
New!!: Integer and Algebraic number theory ·
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 ·
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 ·
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.
In mathematics, the associative property is a property of some binary operations.
New!!: Integer and Associative property ·
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 ·
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 ·
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 ·
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 ·
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) ·
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
New!!: Integer and Cardinality ·
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 ·
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) ·
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
New!!: Integer and Commutative property ·
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 ·
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 ·
In algebra, a cyclic group is a group that is generated by a single element.
New!!: Integer and Cyclic group ·
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 ·
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 ·
In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from elementary algebra.
New!!: Integer and Distributive property ·
In mathematics, especially in elementary arithmetic, division (denoted ÷ or / or —) is an arithmetic operation.
New!!: Integer and Division (mathematics) ·
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 ·
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) ·
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) ·
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 ·
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 ·
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 ·
. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.
New!!: Integer and Euclidean algorithm ·
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 ·
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 ·
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 ·
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) ·
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 ·
In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively.
A fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.
New!!: Integer and Fraction (mathematics) ·
French (le français or la langue française) is a Romance language, belonging to the Indo-European family.
New!!: Integer and French language ·
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.
Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician.
New!!: Integer and Garrett Birkhoff ·
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 ·
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 ·
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) ·
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 ·
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 ·
In non-standard analysis, a hyperinteger N is a hyperreal number equal to its own integer part.
New!!: Integer and Hyperinteger ·
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 ·
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 ·
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.
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 ·
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 ·
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.
New!!: Integer and Integer sequence ·
In mathematics, an integer-valued function is a function whose values are integers.
New!!: Integer and Integer-valued function ·
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 ·
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 ·
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.
Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.
New!!: Integer and Latin ·
This is a list of symbols found within all branches of mathematics to express a formula or to represent a constant.
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 ·
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 ·
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 ·
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 ·
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 ·
A number is a mathematical object used to count, measure and label.
New!!: Integer and Number ·
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 ·
The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.
In mathematics, an ordered pair (a, b) is a pair of mathematical objects.
New!!: Integer and Ordered pair ·
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 ·
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 ·
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 ·
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 ·
A programming language is a formal constructed language designed to communicate instructions to a machine, particularly a computer.
New!!: Integer and Programming language ·
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 ·
In mathematics, a real number is a value that represents a quantity along a continuous line.
New!!: Integer and Real number ·
In mathematics, the remainder is the amount "left over" after performing some computation.
New!!: Integer and Remainder ·
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) ·
In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.
New!!: Integer and Ring homomorphism ·
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 ·
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 ·
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
New!!: Integer and Set (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) ·
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 ·
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 ·
Subtraction is a mathematical operation that represents the operation of removing objects from a collection.
New!!: Integer and Subtraction ·
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 ·
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 ·
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 ·
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 ·
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 ·
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 ·
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 ·
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 ·
The Wolfram Demonstrations Project is hosted by Wolfram Research, whose stated goal is to bring computational exploration to the widest possible audience.
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 ·
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) ·
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... ·
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) ·
Construction of the integers, Discrete number, Entier relatif, Integar, Integer number, Integer numbers, Integer value, Integer-valued, IntegerNumbers, Integers, Intergar, Interger, Negative integer, Rational integer, Ring of rational integers, Set of integers, Signed Numbers, Z (set), Zahlen, ℤ.