# E^(-i * x) not well-defined. Why?

 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 E^(-i * x) not well-defined. Why? The standard definition of "function" for real numbers requires that "if x= y, then f(x)= f(y)"- i.e. that f is "well-defined". For functions of complex variables, that is simply too restrictive. "Functions" that we would like to be able to use, such as $e^x$ would no longer be "functions". So we drop that requirement.