This is obviously true, but I can't quite prove it.
If $f : [a, b] \to \mathbb{R}$ is non-monotonic and continuous, there exists distinct $u,v \in [a, b]$ such that $f(u) = f(v)$
Any help is appreciated.
This is obviously true, but I can't quite prove it.
If $f : [a, b] \to \mathbb{R}$ is non-monotonic and continuous, there exists distinct $u,v \in [a, b]$ such that $f(u) = f(v)$
Any help is appreciated.