PocketMatrix

Bump!

So, anyone wants to solve maths problems this weekend? Here's your chance! It's not exactly rocket science, but I'm not sure if there's a solution to the following problem:

f(x,y) = arctan(|y/x|) is a continuous function. Can it be extended to be a continuous function defined in all of R^2?

I'm thinking you could define it as for example:
f(x,y) = arctan(|y/x|) when x!=0 and
(π/2) - arctan(|x/y|) when x = 0 && y!=0

But it is still not continuous in (0,0). If I approach (0,0) along the x-axis, f approaches 0, while it seems to approach (π/4) if I go diagonally (t,t) -> (0,0). So is the answer simply no, or am I missing something? Thoughts?

P.S Yes this is for a university course, but cooperation is encouraged by the professor

This is indeed a pressing problem, and consequently I will put the full weight of my undergraduate education behind addressing it. Behold, now, the practical value of the philosophy degree:

Mathematics is simply a category of understanding that humans, by necessity, apply to reality in order to 'construct' a way of understanding it. It's a fiction that we created out of a lack of any other way to behold and explain natural phenomena.

Take that, math majors!