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Unformatted text preview: , 1) and [0 , 1]. Prove that the function you found is a bijection. 5. Prove that the function f : (0 , 1) R ,f ( x ) = 2 x1 2 x (1x ) is a bijection between (0 , 1) and R . 6. Bonus Question! Prove that every natural number n 2 can be written as a sum of dierent Fibonacci numbers such that the sum does not include any two consecutive Fibonacci numbers. (For example, 2 = F 3 , 3 = F 4 , 4 = F 4 + F 2 , 5 = F 5 , 6 = F 5 + F 2 , 7 = F 5 + F 3 , 8 = F 6 , 9 = F 6 + F 2 , 10 = F 6 + F 3 , 11 = F 6 + F 4 , 12 = F 6 + F 4 + F 2 , 13 = F 7 etc.)...
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This note was uploaded on 12/07/2011 for the course MATH 245 taught by Professor Cioaba during the Fall '10 term at University of Delaware.
 Fall '10
 CIOABA
 Math

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