(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Analysis of Continuous functions

**Physics Forums | Science Articles, Homework Help, Discussion**