There is nothing mysterious. Endofunctions on sets are transformations. Think permutations but you are allowed to have repeats. If you iterate them f(x), f(f(x)

There is nothing mysterious. Endofunctions on sets are transformations. Think permutations but you are allowed to have repeats. If you iterate them f(x), f(f(x)), f(f(f(x))) ... the function forgets elements until you have a stable partition which cycles. http://chadbrewbaker.github.io/combinatorics/transformations/permutations/2014/08/07/endo.html http://chadbrewbaker.github.io/combinatorics/transformations...