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Let $S$ be a collection of real numbers (written $S\subseteq \mathbb{R}$, or $S$ is a subset of the real numbers).

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.

Page last modified on January 07, 2019, at 02:47 PM

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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 Please Login to access more options. Definition (Lower Bound, Upper Bound, Bounded) Let $S$ be a collection of real numbers (written $S\subseteq \mathbb{R}$, or $S$ is a subset of the real numbers). 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. Edit Page History Source Attach File Backlinks List Group Page last modified on January 07, 2019, at 02:47 PM
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