A short way to say f(f(f(f(x)))) Is there a short way to say $f(f(f(f(x))))$?
I know you can use recursion:
$g(x,y)=\begin{cases}
f(g(x,y-1)) & \text{if } y > 0, \
\newline x & \text{if } y = 0.
\end{cases}$

You should define it this way:
$$
\begin{eqnarray}
\text{iterate}_0(f) &:=& id \\
\text{iterate}_{n + 1}(f) &:=& \text{iterate}_{n}(f) \circ f
\end{eqnarray}
$$
Then write $\text{iterate}_4(f)(x)$.
