Question

设函数在f(z)在z0连续,且f(z0)不等于0,证明可找到z0的小邻域使在小邻域内f(z)不等于0

Answer 1

因为f(x)在z0处连续,即|f(z)|在z0处连续,所以lim(z-->z0)|f(z)|=|f(z0)|.

由极限的定义可知,对任意小的正数a,总存在正实数b,当|z-z0|