(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f : R → R be continuous on R and assume that P = {x ∈ R : f(x) > 0} is non-empty. Prove that for any x0 ∈ P there exists a neighborhood Vδ(x0) ⊆ P.

2. Relevant equations

3. The attempt at a solution

If you choose some x, y ∈ P, since f(x) is continuous then |f(x) - f(y)| < ε for some ε>0

then |x-y|<δ for some δ(ε)

I don't really know where I'm going with this, but I know it has something to do with the question...

Can someone point me in the right direction?

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# Analysis of Continuous functions

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