# Continuous functions

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A- Show that if a function is continuous on all of R and equal to 0 at every rational point then it must be identically 0 on all of R

b- if f and g are continuous on all of R and f(r)=g(r) at every rational point,must f and g be the same function?

https://brainmass.com/math/real-analysis/continuous-functions-29172

#### Solution Preview

a. Proof:

For any irrational point x, we can always find a sequence of rational points x_n such that x_n->x as n->oo. From the definition, ...

#### Solution Summary

There are two proofs regarding rational points and continuity of functions.

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