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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- Oct 20th 2009, 04:19 PMgixxer998Show 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. - Oct 20th 2009, 04:55 PMJose27
Let such that and is continous at then For there exist a such that whenever . And so with this we have