In this video, we explore cycle composition in S_4. Note, the binary operation in S_4 is "composition" not multiplication. I emphasize this because...just like in Precalculus when we performed (fog)(x)=f(g(x)), we started our calculations from right to left. We work on the innermost function first. The same is true in S_n. For an excellent discussion of this topic, see Dummit and Foote's Abstract Algebra text, pg. 31
