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Unformatted text preview: > 0 such that c p,q k x k p k x k q d p,q k x k p , x R n . 7. Let ( X, d ) be a metric space, and A X . Dene the distance from x to A by d ( x , A ) = inf d ( x , y ) y A . Prove that d ( x , A )d ( y , A ) d ( x , y ) x , y X. 1 2 8. Let 0 < x 1 < y 1 . For n 1, set x n +1 = x n y n , y n +1 = 1 2 ( x n + y n ) . Show that lim x n and lim y n exist and are equal. ( Hint: Check that < x n < y n , y n +1 < y n , and x n < x n +1 ) ....
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 Fall '08
 Stopple,J
 Limits

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