Prove that the supremum of a set is in the set – math.stackexchange.com

Prove that the supremum of a set is in the set – math.stackexchange.com

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Let $f$ be a function having the intermediate value property (it is not necessarily continuous) and $y \in \mathbb{R}$ is fixed. It is given that $$M=\{x \in \mathbb{R} \mid f(x)=y \}$$ is bounded ...

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