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- Abelian group : A group in which the group operation is commutative.
- Algebraic number field : A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory.
- Algebraic number : A complex number that is a root of a polynomial with rational coefficients.
- Algebra : A branch of mathematics concerning the study of structure, relation and quantity.
- An elementary proof that 22 over 7 exceeds π : Add brief definition or description
- Associativity : A property of an algebraic operation such as multiplication: a(bc) = (ab)c.
- Commutativity : A property of a binary operation (such as addition or multiplication), that the two operands may be interchanged without affecting the result.
- Conductor of a number field : Used in algebraic number theory; a modulus which determines the splitting of prime ideals.
- Connected space : A topological space in which there is no non-trivial subset which is both open and closed.
- Coprime : Integers, or more generally elements of a ring, which have no non-trivial common factor.
- Cubic equation : A polynomial equation with of degree 3 (i.e., x3+px2+qx+r=0).
- Denseness : A set is dense in another set if the closure of the former set equals the latter set.
- E (mathematics) : Constant real number equal to 2.71828 18284 59045 23536... that is the base of the natural logarithms.
- Equation (mathematics) : 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.
- Exponent : 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.
- Field (mathematics) : An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
- Field automorphism : An invertible function from a field onto itself which respects the field operations of addition and multiplication.
- Fraction (mathematics) : 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).
- Group (mathematics) : 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.
- Heine–Borel theorem : In Euclidean space of finite dimension with the usual topology, a subset is compact if and only if it is closed and bounded.
- Integer : The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.
- Integral domain : A commutative ring in which the product of two non-zero elements is again non-zero.
- Irrational number : A real number that cannot be expressed as a fraction, m / n, in which m and n are integers.
- Mathematics : Add brief definition or description
- Metric space : Add brief definition or description
- Minimal polynomial : Add brief definition or description
- Natural number : Add brief definition or description
- Number : Add brief definition or description
- Ordered field : Add brief definition or description
- Ordered pair : Add brief definition or description
- P-adic metric : Add brief definition or description
- Polynomial : Add brief definition or description
- Quadratic field : Add brief definition or description
- Rational function : Add brief definition or description
- Real number : Add brief definition or description
- Ring (mathematics) : Add brief definition or description
- Set (mathematics) : Add brief definition or description
- Subspace topology : Add brief definition or description
- Transcendental number : Add brief definition or description