Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

This question already has an answer here:

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!

share|improve this question

marked as duplicate by amWhy, user61527, mt_, Asaf Karagila, Davide Giraudo Jun 25 at 16:21

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
Were the answers on this similar question not to your liking? –  The Chaz 2.0 Mar 1 '12 at 14:07
    
Also, this –  The Chaz 2.0 Mar 1 '12 at 14:12
    
Thanks for pointing these out. They didn't come up whilst writing the question, but I should have exercised more due diligence. Apologies! –  xlm Mar 1 '12 at 14:19

1 Answer 1

up vote 1 down vote accepted

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 $f$.

share|improve this answer
    
Thanks Chris. However does $f^0(x)$ = x? Or does it also have multiple meanings? –  xlm Mar 1 '12 at 14:27
    
Well, I suppose it might mean the constant function $1$. But I wasn't sure about its usage, so I left it out. –  Chris Eagle Mar 1 '12 at 14:30

Not the answer you're looking for? Browse other questions tagged or ask your own question.