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HelmutKnaust (Talk | contribs) (Created page with "'''Problem 1.''' We say that $m$ is the maximum of a set $A$ if $m\in A$ and $m\geq a$ for all $a\in A$. Suppose a set $A$ of real numbers has a maximum, call it $m$. Show th...") |
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Latest revision as of 23:21, 14 October 2013
Problem 1. We say that $m$ is the maximum of a set $A$ if $m\in A$ and $m\geq a$ for all $a\in A$.
Suppose a set $A$ of real numbers has a maximum, call it $m$. Show that $m$ is also the supremum of $A$.
Problem 2. Let $A=\{x\in\mathbb{Q}\ |\ x^2\leq 3\}$. Show that A is bounded from above, but that $A$ has no maximum.
