Definition:Extension of Sequence

Definition
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 $\left \langle {a_k} \right \rangle_{k \mathop \in A}$.