Let $S = \{0\}\cup\{1\}\cup \{\frac{1}{4n+7} : n =1,2,\ldots\}$. How to find the number of analytic functions which vanish only on $S$? as i just modify the given question Finding the number of analytic functions which vanish only on a given set.
Options are
a: $\infty$
b: $0$
c: $1$
d: $2$
i think answer will be 1 is its corrects or not ? Pliz tell me
The only function which vanishes on $S$ is the zero function, by the identity theorem, thus there are $0$ functions which vanish only on $S$.