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Unformatted text preview: coordinates. Lemma 2.3.5. Suppose { p i } is a sequence of points in R 3 with respective coordinates ( x i ,y i ,z i ) and L R 3 has coordinates ( 1 , 2 , 3 ) . Then the following are equivalent: 1. p i L (in R 3 ); 2. x i 1 , y i 2 , and z i 3 (in R ). Proof. (1) (2) : Suppose p i L . Given > 0, we can nd N so that i > N guarantees dist( p i ,L ) < . But then by Lemma 2.3.1 max(  x i 1  ,  y i 2  ,  z i 3  ) < , showing that each of the coordinate sequences converges to the corresponding coordinate of L ....
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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, Limits

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