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Unformatted text preview: Show that every decreasing sequence of real numbers that is bounded below converges to its in&mum. (Hint: you can directly use the result of question 4) 6. Metric Space (a) & ( x;y ) = ( 1 if x 6 = y otherwise , prove whether or not it is a metric on R n . (b) & ( x;y ) = P n i =1 j x i & y i j , prove whether or not it is a metric on R n . (c) Suppose ( S 1 ;d 1 ) and ( S 2 ;d 2 ) are metric spaces. Show that ( S 1 ³ S 2 ;& ) is a metric space, where & (( x 1 ; x 2 ) ; ( y 1 ;y 2 )) = max f d 1 ( x 1 ; y 1 ) ;d 2 ( x 2 ;y 2 ) g for all x 1 ;y 1 2 S 1 and all x 2 ; y 2 2 S 2 . 1...
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This note was uploaded on 10/04/2010 for the course ECON 204 taught by Professor Anderson during the Summer '08 term at Berkeley.
- Summer '08