let $$f(x)= \sum_{n=1}^{\infty}a_n x^n$$ where $a_n\in \{0,1\}$, and the $f(x)$ has a natural boundary.
Is $f(x)$ at $\frac{1}{10}$ transcendental?
Is the value of the power series at 0.1 transcendental?
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