Picard's little theorem

Statement

The range of a nonconstant entire function (holomorphic function on the whole of $\mathbb{C}$) can miss at most one point.

Equivalently, any entire function whose range omits two points is a constant.

Relation with other facts

Stronger facts

• Picard's big theorem

Weaker facts

• Bounded and entire implies constant

Other related facts

• Fundamental theorem of algebra