7.9, due April 1

At first I really didn't like the new notation for permutations, but as I kept reading I eventually got used to it and it does seem simpler although I am still really glad that it isn't the notation we used from the beginning. I do not like/understand well the factorization of a permutation. I don't know if I just can't follow what order they are doing them in or what but for some reason when they write out the factorization I can't seem to follow what they've done or how the two sides are equal. Because of this, it was also hard for me to follow the last two proofs of this section.