In real analysis and complex analysis, branches of mathematics, the identity theorem for analytic functions states: given functions f and g analytic on a domain D, if f = g on some S ⊆ D {\displaystyle S\subseteq D}, where S {\displaystyle S} has an accumulation point in D, then f = g on D.Thus an analytic function is completely determined by its values on a single open neighborhood in D, or even a countable subset of D. Wikipedia