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Let m: [0,1) -> [0,1) be the function defined by m(x) = 2x(mod 1). Find a point x element of [0,1) with the property that m2(x) is in a 3-cycle, but m(x) is not. Write your answer as a rational number using decimal points. (Note: this is an example of a pre-periodic point.).

Let m: [0,1) -> [0,1) be the function defined by m(x) = 2x(mod 1). Find a point x element of [0,1) with the property that m2(x) is in a 3-cycle, but m(x) is not. Write your answer as a rational number using decimal points. (Note: this is an example of a pre-periodic point.).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 25E
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Let m: [0,1) -> [0,1) be the function defined by m(x) = 2x(mod 1). Find a point x element of [0,1) with the property that m2(x) is in a 3-cycle, but m(x) is not. Write your answer as a rational number using decimal points. (Note: this is an example of a pre-periodic point.).

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