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Let f:from R to R where R is the reals be continuous on R and let P=:{x exists in R : f(x)>0}.

Let f:from R to R where R is the reals be continuous on R and let P=:{x exists in R : f(x)>0}. If c exists in P, show that there exists a neighborhood Vsub delta(c)is a subset of P

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Since f is continuous at point c ∈ P , and f (c) > 0, Now we know that
for given > 0 there is δ > 0 such that whenever |x − c| < δ we have,
|f (x) − f (c)| <
Then for...

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