Quick check on function composition notation Does $f^n(x)$ always mean $f(f(f(f(...f(x))))....)$ [n times]?
i.e. $f^3(x)$ always means $f(f(f(x)))$?
Does $f^0(x)$ mean $x$? [where $f\neq id$]
By always, I mean regardless of whether it's for proofs in computer science or for calculus.
Just want to be doubly sure so I don't make any unfounded leaps in my proofs by induction for computer science.
Apologies for this simian question.
Many thanks!

No. Sometimes $f^n$ refers to multiplication, rather than composition of functions. This is especially true with trigonometric functions: for example, $\sin^2(x)$ always means $\sin(x) \cdot \sin(x)$, never $\sin(\sin(x))$. Outside trigonometry, composition is a more likely meaning, but multiplication is possible.
Do not confuse either of these with $f^{(n)}$, which means the $n$th derivative of $f$.
