Proving Identity of Continuous Functions on Q

[the_kid]

Homework Statement

Let f and g be two continuous functions defined on R.
I'm looking to prove the fact that if they agree on Q, then f and g are identical.

Homework Equations

The Attempt at a Solution

I'm not really sure where to start with this. Can someone point me in the right direction?

 

[micromass]

What definition of continuity would you like to use??
What characterizations of contintuity do you know??

What's special about $\mathbb{Q}$??