I've heard the statement "Let's just see if starting with 0 or 1 makes the equations and explanations prettier" quite a few times. For example, a sequence <x, f

I've heard the statement "Let's just see if starting with 0 or 1 makes the equations and explanations prettier" quite a few times. For example, a sequence <x, f(x), f(f(x)), ...> is easier to look at if a_0 has f applied 0 times, a_1 has f applied 1 time, and so on.