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    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?

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    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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