Characteristic sequence

In mathematics, the characteristic sequence of a given sequence s is a sequence of 1s and 0s 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 $s_n \in A$:

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