Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm having a conflict with the concept of arity, I've read that the factorial is a unary operation and also that the exponentiation is a binary operation but I feel there's something strange, the definition for exponentiation is:

$$b^n = \underbrace{b \times \cdots \times b}_n$$

And the definition for factorial is:

$$n ! = n \times...\times 1 $$

So, for both exponentiation ($x^n$) and factorial ($n!$) shouldn't $n$ be the arity? Since we need to perform $n$ multiplications in order to evaluate it? With one exception for $0!=1$ which may be a unary operation.

share|cite|improve this question
up vote 7 down vote accepted

When we evaluate the exponential $a^b$ we need two inputs $a$ and $b$. When we evaluate the factorial $n!$ we only need one input $n$.

share|cite|improve this answer
Oh, I thought it had something to do with the number of operations it is needed for evaluating it. – Voyska Nov 24 '12 at 19:59
Check out – Peter Smith Nov 24 '12 at 20:59

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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