Common
Identity theorem
Theorem on the equality of analytic functions
Identity theorem
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 (open and connected subset of R {\displaystyle \mathbb {R} } or C {\displaystyle \mathbb {C} } ), 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 with an accumulation point (provided this contains a converging sequence together with its limit). This is not true in general for real-differentiable functions, even infinitely real-differentiable functions. In comparison, analytic functions are...
Open boosters, collect cards and trade them. Free to play.
Play for free