Maximum and Minimum

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Definition (Maximum and Minimum)

Let $S\subseteq \mathbb{R}$.

• We say $m$ is a minimum of $S$ if $m$ is a lower bound for $S$ and $m\in S$. We write $\min S$ for the minimum of $S$.
• We say $m$ is a maximum of $S$ if $m$ is an upper bound for $S$ and $m\in S$. We write $\max S$ for the maximum of $S$.