Continuous functions

1. Jan 28, 2012

the_kid

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution
I'm not really sure where to start with this. Can someone point me in the right direction?

2. Jan 28, 2012

micromass

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

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