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nondecreasing sequence

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  • Sequence — For other uses, see Sequence (disambiguation). In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length …   Wikipedia

  • Complete sequence — In mathematics, an integer sequence is called a complete sequence if every positive integer can be expressed as a sum of values in the sequence, using each value at most once. For example, the sequence of powers of two {1, 2, 4, 8, ...}, based on …   Wikipedia

  • Beatty sequence — A (homogeneous) Beatty sequence mathcal{B} r, is a sequence formed by successive positive integer multiples of a positive irrational number r, rounded down to the nearest integer, so that the sequence:mathcal{B} r = lfloor r floor, lfloor 2r… …   Wikipedia

  • Tournament (graph theory) — Tournament A tournament on 4 vertices Vertices n Edges …   Wikipedia

  • Daniell integral — In mathematics, the Daniell integral is a type of integration that generalizes the concept of more elementary versions such as the Riemann integral to which students are typically first introduced. One of the main difficulties with the… …   Wikipedia

  • Lebesgue integration — In mathematics, the integral of a non negative function can be regarded in the simplest case as the area between the graph of that function and the x axis. Lebesgue integration is a mathematical construction that extends the integral to a larger… …   Wikipedia

  • Ordinal number — This article is about the mathematical concept. For number words denoting a position in a sequence ( first , second , third , etc.), see Ordinal number (linguistics). Representation of the ordinal numbers up to ωω. Each turn of the spiral… …   Wikipedia

  • Longest increasing subsequence — The longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. This subsequence is not… …   Wikipedia

  • Bolzano–Weierstrass theorem — In real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite dimensional Euclidean space R^n. The theorem states that each bounded sequence in R^n has a convergent subsequence. An equivalent formulation… …   Wikipedia

  • Completeness of the real numbers — Intuitively, completeness implies that there are not any “gaps” (in Dedekind s terminology) or “missing points” in the real number line. This contrasts with the rational numbers, whose corresponding number line has a “gap” at each irrational… …   Wikipedia

  • Stochastic approximation — methods are a family of iterative stochastic optimization algorithms that attempt to find zeroes or extrema of functions which cannot be computed directly, but only estimated via noisy observations. The first, and prototypical, algorithms of this …   Wikipedia

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