Let A be a non-empty set, and let /: AA be a function. Suppose that f...

 

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Let A be a non-empty set, and let /: A→A be a function. Suppose that f is bijective. Suppose further that A is finite; the results in this exercise are valid only for finite sets. Let x, y A. (3) Prove that if f(x)=x for some k = Z, then f (w) = w for all w€ Ox. (4) The stabilizer of x with respect to f, denoted fr, is the set defined by fx = {mEZ | f(x)=x and 0 <m<r}. Suppose that y € O. Prove that fy-fx- Let A be a non-empty set, and let /: A→A be a function. Suppose that f is bijective. Suppose further that A is finite; the results in this exercise are valid only for finite sets. Let x, y A. (3) Prove that if f(x)=x for some k = Z, then f (w) = w for all w€ Ox. (4) The stabilizer of x with respect to f, denoted fr, is the set defined by fx = {mEZ | f(x)=x and 0 <m<r}. Suppose that y € O. Prove that fy-fx-

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answer 3 Suppose fxx for some k Z Since f is a bijection it is an injecti... View the full answer