|October 6th, 2011, 04:48 AM||#1|
Joined: Oct 2011
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.
|element, show, written|
|Thread||Thread Starter||Forum||Replies||Last Post|
|Why in the answer written all discharge||r-soy||Physics||0||March 1st, 2012 08:06 AM|
|Numbers written on a board =) =) =) (3)||Sara so||Algebra||4||January 5th, 2011 07:32 PM|
|Number written on a board =) =)||Sara so||Algebra||4||January 4th, 2011 07:29 AM|
|Numbers written on a board =)||Sara so||Algebra||3||January 3rd, 2011 10:27 PM|
|Help with Written Proofs||mathmajorintrouble||Abstract Algebra||11||May 4th, 2009 11:41 AM|