\begin{definition}[Definition:Sequence/Equality]
Let $f$ and $g$ be two sequences on the same set $A$:
: $f = \left\langle{a_k}\right\rangle_{k \mathop \in A}$
: $g = \left\langle{b_k}\right\rangle_{k \mathop \in B}$
Then $f = g$ {{iff}}:
: $A = B$
: $\forall i \in A: a_i = b_i$
Category:Definitions/Sequences
\end{definition}