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 $s_n \in A$:

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

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