Characteristic sequence

In mathematics, the characteristic sequence of a given sequence s is a sequence of 1's and 0's which tells which elements of s are in some set.

Given two sets $A \subseteq B$ and a sequence s = $\langle s_n : n \in \mathbb{N}\rangle$ of elements of B, the characteristic sequence of s is the sequence $\langle c_n : n \in \mathbb{N}\rangle$ defined so that c_n = 1 if and only if $s_n \in A$:

$c_n = \begin{cases} 0 & s_n \not \in A, \\ 1 & s_n \in A. \end{cases}$

This mathematical logic-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Mathematical logic stubs Mathematical logic Binary sequences Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? Maniac Road $uper $aver Look at other dictionaries: Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued …   Wikipedia Genus of a multiplicative sequence — In mathematics, the genus of a multiplicative sequence is a ring homomorphism, from the cobordism ring of smooth oriented compact manifolds to another ring, usually the ring of rational numbers.DefinitionA genus phi; assigns a number phi;( X ) to …   Wikipedia Potter sequence — Not to be confused with Doege Potter syndrome or Pott s Disease. Potter sequence Classification and external resources ICD 10 Q60.6 ICD 9 …   Wikipedia Light characteristic — Symbols and abbreviations for light characteristics A light characteristic is a graphic and text description of a navigational light sequence or colour displayed on a nautical chart or in a Light List with the chart symbol for a lighthouse,… …   Wikipedia Algorithmically random sequence — Intuitively, an algorithmically random sequence (or random sequence) is an infinite sequence of binary digits that appears random to any algorithm. The definition applies equally well to sequences on any finite set of characters. Random sequences …   Wikipedia Exact sequence — In mathematics, especially in homological algebra and other applications of abelian category theory, as well as in differential geometry and group theory, an exact sequence is a (finite or infinite) sequence of objects and morphisms between them… …   Wikipedia Look-and-say sequence — The lines show the growth of the numbers of digits in the look and say sequences with starting points 23 (red), 1 (blue), 13 (violet), 312 (green). These lines (when represented in a logarithmic scale) tend to straight lines whose slopes coincide …   Wikipedia Ducci sequence — A Ducci sequence is a sequence of n tuples of integers. Given an n tuple of integers (a1,a2,...,an), the next n tuple in the sequence is formed by taking the absolute differences of neighbouring integers: Another way of describing this is as… …   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 Alu sequence — An Alu sequence is a short stretch of DNA originally characterized by the action of the Alu restriction endonuclease. Alu sequences of different kinds occur in large numbers in primate genomes. In fact, Alu sequences are the most abundant mobile… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”