# Math Help - Show a neighborhood exists

1. ## 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.

2. 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 $f(x)>0$