1. The problem statement, all variables and given/known data Prove that the function defined as f(x)= x when x is rational and -x when x is irrational is only continuous at 0. 2. Relevant equations 3. The attempt at a solution I have been looking at this website which proves this: http://planetmath.org/encyclopedia/FunctionContinuousAtOnlyOnePoint.html [Broken] I don't understand how the writer proves that the function is not continuous when a[tex]\neq[/tex]0. Why do they take xk= to something? How does this help them show that the limits equal a and -a. How does showing that prove that f is not continuous at a? I know those are a lot of question, but maybe an answer to even just the first ones would help me understand this proof.