Definition:Sequence/Equality

Definition
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 $f = g$ :
 * $A = B$
 * $\forall i \in A: a_i = b_i$