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Math Help - Show a neighborhood exists

  1. #1
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    Show a neighborhood exists

    R=Reals
    Let f : R --> R be continuous on R, and let P := {x in R : f(x) is greater than 0}. If c is in P, show that there exists a neighborhood V delta(c) as an element of P.
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  2. #2
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    Let p such that r=f(p)>0 and f is continous at p then For \epsilon =r there exist a \delta >0 such that \vert f(p)-f(x) \vert < r whenever \vert x-p \vert < \delta. And so with this \delta we have f(x)>0
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