Limit of a Dirichlet Function

[danshawvassar]

I have a homework assignment due tomorrow that I am having trouble with..

Let f(x)= {2 if x is rational
{-2 if x is irrational

Prove rigorously via "epsilon"-"delta"'s that lim x->3 of f(x) D.N.E. (Does not exist)

 

[tkhunny]

The limit must be either 2 or -2, right? Those are the only two values taken on by the function.

One way might be,
1) Given a rational number close to three, construct an irrational number even closer.
2) Given an irrational number close to three, construct a rational number even closer.

It seems that #2 might be a little harder, but maybe not.