Suppose a function f : R → R is continuous with f(0) = 1. Show that...

Suppose a function f : R → R is continuous with f(0) = 1. Show that if there is a positive number x₀ for which f(x₀) = 0, then there is a smallest positive number p for which f(p) = 0. (Hint: Consider the set {x | x > 0, f(x) = 0}.)

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Colby Messinger answered 1 year ago

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