\begin{definition}[Definition:Extension of Sequence]
As a sequence is, by definition, also a mapping, the definition of an '''extension of a sequence''' is the same as that for an extension of a mapping:
Let:
: $\left \langle {a_k} \right \rangle_{k \mathop \in A}$ be a sequence on $A$, where $A \subseteq \N$.
: $\left \langle {b_k} \right \rangle_{k \mathop \in B}$ be a sequence on $B$, where $B \subseteq \N$.
: $A \subseteq B$
: $\forall k \in A: b_k = a_k$.
Then $\left \langle {b_k} \right \rangle_{k \mathop \in B}$ '''extends''' or '''is an extension of''' $\left \langle {a_k} \right \rangle_{k \mathop \in A}$.
\end{definition}