What does the → notation mean in this context?

Question

Show that f: A ⊂ C → C is continuous if and only if zn → z0 in A implies that f(zn) → f(z0).

Could someone translate this to english for me please? I don't understand what zn → z0 means.

Answer 1

The phrase

$z_n \to z_0$ in $A$ implies that $f(z_n) \to f(z_0)$

is shorthand for

for every sequence $z_1, z_2, \dots$ of elements of $A$ and every element $z_0$ of $A$, if $\lim_{n \to \infty} z_n = z_0$, then $\lim_{n \to \infty} f(z_n) = f(z_0)$.