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October 6th, 2011, 04:48 AM   #1
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Show that every element of G can be written as such?

Given the set of all integers Z (pos, neg, zero), Let G be the set of onto functions T: Z -> Z such that for all m,n in Z we have |T(m) - T(n)| = |m - n|.

Let M, F be elements of G given by M(k) = k +1 and F(n) = -n.

Show that every element of G can be written as M^n or M^(n)F where n can be any integer. Do this by letting n = T(0) and epsilon = T(1) - n. Show that epsilon must be +/-1, and prove that if epsilon = 1, T = M^n, if epsilon = -1, then T = MF.
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