[qmalzp]

Fun fact: compositions of the two operations

x -> x + 1

and

x -> (x==0) ? 1 : (x == 1) ? 0 : x

generate all possible operations.

[rbehrends]

Well, this is just a roundabout way of stating that the symmetric group S_n is generated by (1, 2) and (1, 2, ..., n) for all n. :)