Composition_of_Sequence_with_Mapping

Let $\left \langle {a_j} \right \rangle_{j \in B}$ be a sequence. Let $\sigma: A \to B$ be a mapping, where $A \subseteq \N$. Then $\left \langle {a_j} \right \rangle \circ \sigma$ is a sequence whose value at each $k \in A$ is $a_{\sigma \left({k}\right)}$. Thus $\left \langle {a_j} \right \rangle \circ \sigma$ is denoted $\left \langle {a_{\sigma \left({k}\right)}} \right \rangle_{k \in A}$.