Editing Arity (section)

=== ''n''-ary ===
The [[arithmetic mean]] of ''n'' real numbers is an ''n''-ary  function: <math>\bar{x}=\frac{1}{n}\left (\sum_{i=1}^n{x_i}\right) = \frac{x_1+x_2+\dots+x_n}{n}</math>

Similarly, the [[geometric mean]] of ''n'' [[positive real numbers]] is an ''n''-ary function: <math>\left(\prod_{i=1}^n a_i\right)^\frac{1}{n} = \ \sqrt[n]{a_1 a_2 \cdots a_n} .</math> Note that a [[logarithm]] of the geometric mean is the arithmetic mean of the logarithms of its ''n'' arguments

From a mathematical point of view, a function of ''n'' arguments can always be considered as a function of a single argument that is an element of some [[product space]]. However, it may be convenient for notation to consider ''n''-ary functions, as for example [[multilinear map]]s (which are not linear maps on the product space, if {{nowrap|''n'' ≠ 1}}).

The same is true for programming languages, where functions taking several arguments could always be defined as functions taking a single argument of some [[object composition|composite type]] such as a [[tuple]], or in languages with [[higher-order function]]s, by [[currying]].