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Unformatted text preview: (14 points, Exercise 25(b) on p.102). Let be an irrational real number. Let C 1 be the set of all integers, let C 2 be the set of all n with n C 1 . Show that the algebraic sum C 1 + C 2 := { x = x 1 + x 2 : x 1 C 1 , x 2 C 2 } is not closed in R . #4. (14 points). Let f ( x ) be a function on R , which is continuous at each rational point q R . Show that f ( x ) is continuous at some irrational points....
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This document was uploaded on 02/15/2012.
 Fall '09
 Math

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