I was thinking about the problem that says:
Let $S$ be the open unit disk and $f:S\to \Bbb C$ be a real-valued analytic function with $f(0)=1$.Then which of the following option is correct?
The set $\{z \in S:f(z) \neq 1\}$ is:
(a) empty,
(b) non-empty finite,
(c) countably infinite,
(d) uncountable.
Please help.