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

A lower bound for $S$ is a real number $m$ such that $m\leq x$ for every $x\in S$. We say that $S$ is bounded below if it has a lower bound.
An upper bound for $S$ is a real number $m$ such that $m\geq x$ for every $x\in S$. We say that $S$ is bounded above if it has an upper bound.
We say that $S$ is bounded if has both a lower and upper bound.
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 bound for $S$ and $m\in S$. We write $\max S$ for the maximum of $S$.

Page last modified on June 29, 2016, at 10:45 AM

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HomePage Schedule Pictures Writing Tips LaTeX Commands External Resources List of Problems List of Definitions List of Theorems List of Conjectures All Recent changes (use this to find a page that may have been lost)	Definition Lower Bound, Upper Bound, Bounded, Maximum, Minimum Please Login to access more options. Definition (Lower Bound, Upper Bound, Bounded, Maximum, Minimum) Let $S\subseteq \mathbb{R}$. A lower bound for $S$ is a real number $m$ such that $m\leq x$ for every $x\in S$. We say that $S$ is bounded below if it has a lower bound. An upper bound for $S$ is a real number $m$ such that $m\geq x$ for every $x\in S$. We say that $S$ is bounded above if it has an upper bound. We say that $S$ is bounded if has both a lower and upper bound. 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 bound for $S$ and $m\in S$. We write $\max S$ for the maximum of $S$. Edit Page History Source Attach File Backlinks List Group Page last modified on June 29, 2016, at 10:45 AM
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