Definition:Sequence/Equality

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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 $f = g$ if and only if:

$A = B$
$\forall i \in A: a_i = b_i$