I'm doing some really basic cycle homework, and in doing an exercise, I noticed something which is what i was probably supposed to notice but I want to know if my conclusion is correct. "all mappings from N to N (N=finite subset of naturals) that can be written with exclusively 1 or 2 element cycles are equal to their inverse." For example 1~4, 2~3, 3~2, 4~1 (~ is my quick iPod shorthand for the maps to arrow) is written in cycle notation as (1 4)(2 3) Can I perhaps extend it to: "a mapping from N to N (N= finite subset of naturals) is equal to its inverse iff it can be written with exclusively 1 or 2 element cycles." Can i extend it even more to all finite sets? Ive only done cycles on the naturals so far, I don't know if I'm getting way off here. I'm also trying to think about what these functions look like visually. Does anyone know any good continuous functions that are equal to their inverse besides trivial ones like y=x?