Liouville's theorem (complex analysis)

In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle f} for which there exists a positive number M {\displaystyle M} such that | f ( z ) | ≤ M {\displaystyle |f(z)|\leq M} for all z ∈ C {\displaystyle z\in \mathbb {C} } is constant.