Question: Prove that if is continuous and (a, b) < 0, then there exists a -neighborhood about (a, b) such that (x, y) < 0

Prove that if ƒ is continuous and ƒ(a, b) < 0, then there exists a δ-neighborhood about (a, b) such that ƒ(x, y) < 0
for every point (x, y) in the neighborhood.

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