Unformatted text preview: x . For any sequence ( x n ) in R converging to x , f ( x n ) = x n converges to x trivially. Hence f ( x ) = x is continuous. (ii) Suppose x n is continuous on R , we want to show that x n +1 is also continuous. Note that x n +1 = ( x n ) x. Hence x n +1 is also continuous on R since both x n and x are. By induction, for any n ∈ N , f ( x ) = x n is continuous on R . 1...
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 Spring '10
 GuoliangWu
 Math, Logic, Intermediate Value Theorem, Continuous function, Xn, Connected space

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