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Unformatted text preview: I k s by nonempty open, bounded intervals O k := ( a, b ) = { x R : a < x < b } . 3. A rectangle R is a subset of R 2 of the form R = I J = { ( x, y ) : x I and y J } for some closed, bounded intervals I, J R . Prove that if R 1 R 2 R 3 . . . is a nested sequence of rectangles, then T k =1 R k is nonempty....
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 Fall '09
 Forde

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