Multiple function values for a single x-value I'm curious if it's possible to define a function that would have more than two functionvalues for one single x-value. 
I know that it's possible to get two y-values by using the root (one positive, one negative: $\sqrt{4} = -2 ; +2$).
Is it possible to get three or more function values for one single x-value?

Let's consider some multivalued functions (not 'functions' since these are one to one by definition) :
$y=x^n$ has $n$ different solutions $\sqrt[n]{y}\cdot e^{2\pi i \frac kn}$  (no more than two will be real)
The inverse of periodic functions will be multivalued (arcsine, arccosine and so on...) with an infinity of branches (the principal branch will usually be considered and the principal value returned).
The logarithm is interesting too (every branch gives an additional $2\pi i$).
$i^i$ has an infinity of real values since $i^i=(e^{\pi i/2+2k \pi i})^i=e^{-\pi/2-2k \pi}$ (replace one of the $i$ by $ix$ to get a multivalued function).
The Lambert W function has two rather different branches $W_0$ and $W_{-1}$ 
and so on... 
