I have never liked problems of the sort where rational/irrational numbers are involved.

For the function

determine where

is continuous and where

is discontinuous. Does

have any partial derivatives?

A note provided is as follows: Every neighborhood in

always contains points with rational and points with irrational coordinates.

Mainly, the part I have difficulty with is the rational/irrational bit. I've never been able to work with those properly, probably because I missed something fundamental in my earlier years.