Can a multivalued function have an infinite number of values for a given argument? I'm trying to gain some perspective on complex analysis, and there's this concept of multivalued function which is weird to me because I'm used to functions having only 1 value for an argument, though I think that a multivalued function is not technically a function. So the question is, as indicated in the title: Can a multivalued function have an infinite number of values for a given argument?

In some sense yes. $\ln(1)=2\pi ik$ for every $k \in \mathbb{Z}$.
