Let $f$ be a function of $x$ that respects these conditions: $f(a_n)=0,f(0)=1, n \in [1,\infty) $. From this, can we express the function $f$ as an infinite product? If so, is this statement true?
$$f(x)=\prod_{n=1}^\infty \left(1-\frac{x}{a_n}\right)$$