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 $s_{n}\in A$:

$c_{n}={\begin{cases}0&s_{n}\not \in A,\\1&s_{n}\in A.\end{cases}}$