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A complete metric is a metric in which every Cauchy sequence is convergent. A topological space with a complete metric is called a complete metric space.

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...

A periodic sequence such as {1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, ...} that is periodic from some point onwards.

Let F_n be the nth Fibonacci number. Then the sequence {F_n}_(n=2)^infty={1,2,3,5,8,...} is complete, even if one is restricted to subsequences in which no two consecutive ...

A polynomial is called logarithmically concave (or log-concave) if the sequence of its coefficients is logarithmically concave. If P(x) is log-convex and Q(x) is unimodal, ...

A Lyndon word is an aperiodic notation for representing a necklace.

Given a Farey sequence with consecutive terms h/k and h^'/k^', then the mediant is defined as the reduced form of the fraction (h+h^')/(k+k^').

The polynomials M_k(x;delta,eta) which form the Sheffer sequence for g(t) = {[1+deltaf(t)]^2+[f(t)]^2}^(eta/2) (1) f(t) = tan(t/(1+deltat)) (2) which have generating function ...

A well-formed formula B is said to be true for the interpretation M (written |=_MB) iff every sequence in Sigma (the set of all denumerable sequences of elements of the ...

A method to obtain a signal C_l(z) with a flat spectrum c(theta;z) (such as a pulse), but having a smaller amplitude than the pulse. ...