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(a) Fix an irrational 6 in G and for n = 0, + 1, +2 ,... let ,, be no reduced modulo 1. Show that 0 ,, @ em= 0n+m, 0 ,, ℮6]=0 ,__, and the 0 ,, are distinct.

Show that (02 ,,: n = 0, + 1 ,... ) and (02n + 1: n = 0, + 1 ,... ) are dense in G.