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A special case of Hölder's sum inequality with p=q=2, (sum_(k=1)^na_kb_k)^2<=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2), (1) where equality holds for a_k=cb_k. The inequality is ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...

Let psi_1(x) and psi_2(x) be any two real integrable functions in [a,b], then Schwarz's inequality is given by |<psi_1|psi_2>|^2<=<psi_1|psi_1><psi_2|psi_2>. (1) Written out ...

The property of being continuous.

A definition assigns properties to some sort of mathematical object. For example, Euclid's Elements starts with a number of definitions, such as "a line is a breadthless ...

A property that passes from a topological space to all its quotient spaces. This is true for connectedness, local connectedness and separability, but not for any of the ...

A function between categories which maps objects to objects and morphisms to morphisms. Functors exist in both covariant and contravariant types.

A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest ...

Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are ...

The number of "arrangements" in an ordering of n items is given by either a combination (order is ignored) or a permutation (order is significant). An ordering (or order) is ...