MATH0007 video 13: sign of a permutation
A transposition is a 2-cycle. Proof that every cycle (a, b, c, d, ...) equals (a, b)(b, c)(c, d) ..... Proof that every permutation is a product of cycles. Definition of even and odd permutations. The sign of a permutation, sign(s), is 1 if s is even and -1 if s is odd. Examples of signs of permutations. sign(st) = sign(s)sign(t). Comment that none of this makes any sense unless we show that there aren't any permutations which are both odd and even at the same time.