Proving Identity of Continuous Functions on Q

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

What's special about \mathbb{Q}??
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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