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 $f = g$ if and only if:
$A = B$
$\forall i \in A: a_i = b_i$