Okay, you can probably guess what my question is based on the title, but I think I already know the answer and I just need some verification.
As a math enthusiast, I've noticed a trend in multivariate functions (functions where domain values are allowed to repeat). For every true function, each x value has at least one y value and vice versa. This only occurs in true functions, however, as opposed to functions created solely for human convenience, like the absolute value function, the ceiling function, or the square wave.
That being said, I've analyzed the error function on a wide variety of numbers (real and imaginary), but I never seemed to generate a real number with a real part greater than one.
After a lot of analyzing, I came to the conclusion that the error function behaves much like the arctangent function, in the sense that as a multivariate function, each x would have multiple y values each equidistant from each other. The logic behind this is, due to the Reimmann sphere model, after infinity, numbers start all over again from negative infinity. Since the error function is the integral of the bell curve from 0 to x, and the bell curve has a finite area evaluated on the real axis, the error function could also be represented as the integral from 0 to infinity to negative infinity back to x. Again, due to the Reimann sphere model, this would make sense. So, by this conclusion,
$$erf^{(-1)}(x)=erf^{(-1)}(x-2)=erf^{(-1)}(x-4)=...$$
But, I still need some verification from other people before I can confirm this. If you could follow along, what do you think?
Your "analysis" of the error function is utterly wrong. The ${\rm erf}z$ is an entire function with an essential singularity at $z=\infty,$ so by Picard's theorem, it takes every complex value, except at most one. I don't know if there is such an exceptional value in this case, but neither do you. The error function is not periodic, though along certain directions, it can be described by Fresnel integrals, so it is oscillatory.
Study mathematics before making such claims.