# 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

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

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

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