Let A R and let f A R be continuous at a point c A Show that for any 0, there exists a neighborhood V(c) of c such that if x y A V(c), then f(x) f(y)

Question: Let A R and let f : A R be continuous at a point c A. Show that for any >

Let A ⊂ R and let f : A → R be continuous at a point c ∈ A. Show that for any ε > 0, there exists a neighborhood Vδ(c) of c such that if x; y ∈ A ∩ Vδ(c), then |f(x) - f(y)| < ε.

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