Naming a function in a paper I'm writing a paper (in physics), and I want use the same name for two related functions that have different domains.  Please allow me to elaborate.
I have function $f: R\longmapsto R$.  I want to define a second function on the set of 2-tuples $f:R\times R \longmapsto R$ where f(x,x) = f(x)f(x).   Here is my question: Can I use the same name for the two functions?  In the context of this paper, it would reduce the amount of notation if I could give these two functions the same name. I would argue that there is no confusion here, because the two functions have different domains.  So from the usage of the function, and the domain, a reader will always know which function being is referring to.  Please comment.  thanks.

It's not uncommon to use the same symbol when you restrict or enlarge the domain of a function, but that's not what you're doing here.  Your function of two variables is not necessarily ever equal to the function of one variable:  $f(x)$ might always be negative and $f(x,y)$ always positive.  How would it look, notation-wise, if you used $F(x,y)$ for the two-variable function?
