# Rational number/Related Articles

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A list of Citizendium articles, and planned articles, about Rational number.

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• Abelian group [r]: A group in which the group operation is commutative. [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]
• Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity. [e]
• An elementary proof that 22 over 7 exceeds π [r]: Add brief definition or description
• Associativity [r]: A property of an algebraic operation such as multiplication: a(bc) = (ab)c. [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]
• Conductor of a number field [r]: Used in algebraic number theory; a modulus which determines the splitting of prime ideals. [e]
• Connected space [r]: A topological space in which there is no non-trivial subset which is both open and closed. [e]
• Coprime [r]: Integers, or more generally elements of a ring, which have no non-trivial common factor. [e]
• Cubic equation [r]: A polynomial equation with of degree 3 (i.e., x3+px2+qx+r=0). [e]
• Denseness [r]: A set is dense in another set if the closure of the former set equals the latter set. [e]
• E (mathematics) [r]: Constant real number equal to 2.71828 18284 59045 23536... that is the base of the natural logarithms. [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]
• 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]
• Field (mathematics) [r]: An algebraic structure with operations generalising the familiar concepts of real number arithmetic. [e]
• Field automorphism [r]: An invertible function from a field onto itself which respects the field operations of addition and multiplication. [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]
• 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]
• Heine–Borel theorem [r]: In Euclidean space of finite dimension with the usual topology, a subset is compact if and only if it is closed and bounded. [e]
• Integer [r]: The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. [e]
• Integral domain [r]: A commutative ring in which the product of two non-zero elements is again non-zero. [e]
• Irrational number [r]: A real number that cannot be expressed as a fraction, m / n, in which m and n are integers. [e]
• Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. [e]
• Metric space [r]: Any topological space which has a metric defined on it. [e]
• Minimal polynomial [r]: The monic polynomial of least degree which a square matrix or endomorphism satisfies. [e]
• Natural number [r]: An element of 1, 2, 3, 4, ..., often also including 0. [e]
• Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring. [e]
• Ordered field [r]: A field with a total order which is compatible with the algebraic operations. [e]
• Ordered pair [r]: Two objects in which order is important. [e]
• P-adic metric [r]: A metric on the rationals in which numbers are close to zero if they are divisible by a large power of a given prime p. [e]
• Polynomial [r]: A formal expression obtained from constant numbers and one or indeterminates; the function defined by such a formula. [e]
• Quadratic field [r]: A field which is an extension of its prime field of degree two. [e]
• Rational function [r]: Function that can be expressed as a quotient of polynomials, excluding division by zero. [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]
• Set (mathematics) [r]: Informally, any collection of distinct elements. [e]
• Subspace topology [r]: An assignment of open sets to a subset of a topological space. [e]
• Transcendental number [r]: A number which is not algebraic: that is, does not satisfy any polynomial with integer or rational coefficients. [e]