- 7

- 0

y=x^2

as a simple example. So for an inverse to exist we have to restrict the domain to (0,+infty) right (doesnt matter which branch Im taking, so Ill take this one.)

Now my problem is the point 0, because the point (0) is actually a multiset. For

y=x^2

there is a double zero. So formally speaking the mapping of the origin is (0,0) -> (0). Is this correct? Because if it is, then this implies that the point y=0 has no inverse, regardless of our choice of branch, because there is no bijection at this point.

That is my query. The point (0) is a branch point isnt it? So Im thinking that the inverse doesnt exist here. Is this correct? I've looked online and many sources say that if you restrict the domain to [0,+infty) you get an acceptable inverse, but I think it should be (0,+infty).

Any help that anyone could give would be excellent. Im not being pedantic, this is important for what I am doing. Also sorry if some of my maths definitions are ambiguous; Im a physicist not a mathematician!

Thank you,

Stephen