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Unformatted text preview: x i k 1 R . Now, consider the (sub)sequence oF points { p i k } , and look at their second coordinates. We have  y i k  < M For all i k and hence passing to a sub(sub)sequence, we have y i k 2 R . Note that passing to a subsequence does not afect convergence oF the Frst coordinates: x i k 1 . In a similar way, the third coordinates are bounded v v v z i k v v v < M For all i k and hence we can nd a convergent sub(subsub)sequence { p i k } For which the third coordinates converge as well: z i k 3 R ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus

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