Riemann Hypothesis/Analytical continuation

Definition 1

Suppose $f$ is an analytic function defined on some non-empty open subset of $\mathbb {C}$, $\mathbb {A}$. Suppose $\mathbb {B}$ is also an open subset of $\mathbb {C}$ with cardinality greater than that of $\mathbb {A}$, containing all elements of $\mathbb {A}$. If $g$ is also an analytic function, defined on $\mathbb {B}$, such that,

$f(s)=g(s)\forall s\in \mathbb {A}$

then $g$ may be called an analytical continuation of $f$.