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\lhead{\bf Advanced Calculus (MAA 4211)}
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\rhead{Due Friday 9/2}
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\begin{enumerate}

\Problem Let $A$ be a nonempty set of real numbers which is bounded both above and below. Prove that $\inf(A)\le\sup(A)$.

\Problem Suppose $A$ and $B$ are nonempty sets of real numbers which are both bounded above. Define
\[
	A+B = \{a+b\st a\in A, b\in B\}.
\]
Prove that $A+B$ has a least upper bound and that $\sup(A+B)=\sup(A)+\sup(B)$.

\end{enumerate}

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