HW9 - X be an injective function. Dene a sequence of...

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Name: Math 100 Due Wednesday, December 5, 2:00 pm Homework 9! 1. (3 points) Prove that the following sentence is true: x Z , if x is odd, then y Z , such that xy 1 (mod 16) . Hint: Let R be the set of odd numbers between 1 and 15. Let x be an odd integer, and consider the function from R to R given by: f ( r ) = the remainder left after dividing rx by 16 , for every r R . 2. (2 points) Prove that the following sentence is true: x R , y Z , if y 6 = 1 , then ( y + 1) / ( y - 1) < x. 3. (3 points) Let X be a set. Let f : X
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Unformatted text preview: X be an injective function. Dene a sequence of functions, called g n : X X , for all n N , by the following rule: When n = 0, and x X , then we dene g ( x ) = x . If n 1, and x X , then we dene g n ( x ) = f ( g n-1 ( x )). In other words, g n is the function obtained by repeating the function f , n times. Prove that, for every n N , the function g n is injective....
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This homework help was uploaded on 04/17/2008 for the course MATH 100 taught by Professor Weissman during the Fall '08 term at UCSC.

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