6.4. Topology and Continuity

Theorem 6.4.10: Intermediate Value Theorem

If f is continuous on a closed interval [a, b] and d is any number between f(a) and f(b). Then there exists a number c in the open interval (a, b) such that f(c) = d.


With the work we have done so far this proof is easy. In fact, the easiest proof is an application of Bolzano's theorem, and is left as an exercise.

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