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\leftline{Mathematics 242 -- Principles of Analysis}
\leftline{Definitions Quiz 9 -- April 29, 2011}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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A) (10) Let $f$ be a bounded function on $[a,b]$ and given
$$\eqalign{
\underline{\int}_{\,\,a}^b f &= 
{\rm lub} \{ L_{\cal P}(f) \mid {\cal P} {\rm\ a\ partition\ of\ } [a,b]\}\cr
\overline{\int}_a^{\,\,b} f &= 
{\rm glb} \{ U_{\cal P}(f) \mid {\cal P} {\rm\ a\ partition\ of\ } [a,b]\}.\cr}$$
What does it mean to say that $f$ is {\it integrable} on $[a,b]$?
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B) (10) What does the Axiom of Completeness for ${\bf R}$ say?
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