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# Integer/Related Articles

From Citizendium

< Integer

*See also changes related to Integer, or pages that link to Integer or to this page or whose text contains "Integer".*

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- 0 (number) [r]: A real number and is the integer between 1 and -1, which signifies a value of nothing.
^{[e]} - Abelian group [r]: A group in which the group operation is commutative.
^{[e]} - Adder (electronics) [r]: A digital circuit that performs integer addition in the Arithmetic Logic Unit in a computer.
^{[e]} - Algebraic number field [r]: A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory.
^{[e]} - Algebraic number [r]: A complex number that is a root of a polynomial with rational coefficients.
^{[e]} - Arithmetic function [r]: A function defined on the set of positive integers, usually with integer, real or complex values, studied in number theory.
^{[e]} - Associativity [r]: A property of an algebraic operation such as multiplication: a(bc) = (ab)c.
^{[e]} - Basis (linear algebra) [r]: A set of vectors that, in a linear combination, can represent every vector in a given vector space or free module, and such that no element of the set can be represented as a linear combination of the others.
^{[e]} - Bijective function [r]: A function in which each possible output value corresponds to exactly one input value.
^{[e]} - Binomial theorem [r]: for any natural number
*n*.^{[e]} - Commutativity [r]: A property of a binary operation (such as addition or multiplication), that the two operands may be interchanged without affecting the result.
^{[e]} - Countable set [r]: A set with as many elements as there are natural numbers, or less.
^{[e]} - Cubic reciprocity [r]: Various results connecting the solvability of two related cubic equations in modular arithmetic, generalising the concept of quadratic reciprocity.
^{[e]} - Cyclic group [r]: A group consisting of the powers of a single element.
^{[e]} - Cyclotomic polynomial [r]: A polynomial whose roots are primitive roots of unity.
^{[e]} - Data structure [r]: A means of specifying how information is arranged on storage media for processing.
^{[e]} - Diophantine equation [r]: Equation in which the unknowns are required to be integers.
^{[e]} - Divisibility [r]: A concept in elementary arithmetic dealing with integers as products of integers
^{[e]} - Divisor [r]: The quantity by which another quantity is divided in the operation of division.
^{[e]} - Equation (mathematics) [r]: A mathematical relationship between quantities stated to be equal, seen as a problem involving variables for which the solution is the set of values for which the equality holds.
^{[e]} - Equivalence relation [r]: A reflexive symmetric transitive binary relation on a set.
^{[e]} - Euclid's lemma [r]: A prime number that divides a product of two integers must divide one of the two integers.
^{[e]} - Euclidean algorithm [r]: Algorithm for finding the greatest common divisor of two integers
^{[e]} - Exact sequence [r]: A sequence of algebraic objects and morphisms which is used to describe or analyse algebraic structure.
^{[e]} - Exponent [r]: A mathematical notation used to represent the operation of exponentiation. It is usually written as a superscript on a number or variable, called the base. For example, in the expression, the base is 5 and the exponent is 4.
^{[e]} - Fermat's last theorem [r]: Theorem that the equation an + bn = cn has no solutions in positive integers a, b, c if n is an integer greater than 2.
^{[e]} - Field (mathematics) [r]: An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
^{[e]} - Fraction (mathematics) [r]: A concept used to convey a proportional relation between a part and the whole consisting of a numerator (an integer — the part) and a denominator (a natural number — the whole).
^{[e]} - Free group [r]: A group in which there is a generating set such that every element of the group can be written uniquely as the product of generators.
^{[e]} - Group (mathematics) [r]: Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation.
^{[e]} - Group theory [r]: Branch of mathematics concerned with groups and the description of their properties.
^{[e]} - History of music psychology [r]: Description of the historical development of research in music psychology.
^{[e]} - Irrational number [r]: A real number that cannot be expressed as a fraction, m / n, in which m and n are integers.
^{[e]} - Least common multiple [r]: The smallest integer which is divided evenly by all given numbers.
^{[e]} - Linear equation [r]: Algebraic equation, such as y = 2x + 7 or 3x + 2y − z = 4, in which the highest degree term in the variable or variables is of the first degree.
^{[e]} - Mathematics [r]: The study of quantities, structures, their relations, and changes thereof.
^{[e]} - Measure (mathematics) [r]: Systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset.
^{[e]} - Module [r]: Mathematical structure of which abelian groups and vector spaces are particular types.
^{[e]} - Molecule [r]: An aggregate of two or more atoms in a definite arrangement held together by chemical bonds.
^{[e]} - Monoid [r]: An algebraic structure with an associative binary operation and an identity element.
^{[e]} - Multiple (mathematics) [r]: The product of an integer with another integer.
^{[e]} - Natural number [r]: An element of 1, 2, 3, 4, ..., often also including 0.
^{[e]} - Noetherian ring [r]: A ring satisfying the ascending chain condition on ideals; equivalently a ring in which every ideal is finitely generated.
^{[e]} - Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring.
^{[e]} - Order (group theory) [r]: For a group, its cardinality; for an element of a group, the least positive integer (if one exists) such that raising the element to that power gives the identity.
^{[e]} - Particle in a box [r]: A system in quantum mechanics used to illustrate important features of quantum mechanics, such as quantization of energy levels and the existence of zero-point energy.
^{[e]} - Partition (mathematics) [r]: Concepts in mathematics which refer either to a partition of a set or an ordered partition of a set, or a partition of an integer, or a partition of an interval.
^{[e]} - Pascal's triangle [r]: A convenient tabular presentation for the binomial coefficients.
^{[e]} - Pitch (music) [r]: Perceived frequency of a sound or musical tone.
^{[e]} - Polynomial [r]: A formal expression obtained from constant numbers and one or indeterminates; the function defined by such a formula.
^{[e]} - Prime number [r]: A number that can be evenly divided by exactly two positive whole numbers, namely one and itself.
^{[e]} - Quadratic equation [r]: An equation of the form
*ax*^{2}+*bx*+*c*= 0 where*a*,*b*and*c*are constants.^{[e]} - Rational number [r]: A number that can be expressed as a ratio of two integers.
^{[e]} - Reaction rate [r]: The amount of reactant or product that is formed or removed (in moles or mass units) per unit time per unit volume, in a particular reaction.
^{[e]} - Real number [r]: A limit of the Cauchy sequence of rational numbers.
^{[e]} - Ring (mathematics) [r]: Algebraic structure with two operations, combining an abelian group with a monoid.
^{[e]} - Ring homomorphism [r]: Function between two rings which respects the operations of addition and multiplication.
^{[e]} - Semigroup [r]: An algebraic structure with an associative binary operation.
^{[e]} - Set (mathematics) [r]: Informally, any collection of distinct elements.
^{[e]} - Simplex [r]: A geometrical body, generalization of the triangle (plane) and the 3-sided pyramid (space) to arbitrary dimensions.
^{[e]} - Square root of two [r]: The positive real number that, when multiplied by itself, gives the number 2.
^{[e]} - Stack [r]: Abstract data type in computer science that supports last-in first-out (LIFO) access to its contents.
^{[e]} - Structure (mathematical logic) [r]: A set along with a collection of finitary functions and relations which are defined on it.
^{[e]} - Transcendental number [r]: A number which is not algebraic: that is, does not satisfy any polynomial with integer or rational coefficients.
^{[e]} - Transitive relation [r]: A relation with the property that if x→y and y→z then x→z.
^{[e]} - Trigonometric function [r]: Function of an angle expressed as the ratio of two of the sides of a right triangle that contains that angle; the sine, cosine, tangent, cotangent, secant, and cosecant.
^{[e]}