 If the set of zeros of an analytic function ƒ has an accumulation point inside its domain, then ƒ is zero everywhere on the connected component containing the accumulation point.In other words, if ("rn") is a sequence of distinct numbers such that ƒ("r""n") = 0 for all "n" and this sequence converges to a point "r" in the domain of "D", then ƒ is identically zero on the connected component of "D" containing "r".This is known as the Principle of Permanence.