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A function whose \trefi[functions]{domain} is a
\trefii[cartesian-product]{Cartesian}{product} can be seen as a function taking
multpile \trefis[functions]{argument}. The \defi{arity} (also called
\defi[name=arity]{rank}, \defi[name=arity]{adicity}, \defi[name=arity]{valency}.
\defi[name=arity]{rank}, \defi[name=arity]{adicity}, \defi[name=arity]{valency}).
$\fun{f}{\ncartli{A}1k}{B}$ is $k$.
\end{definition}
\begin{definition}
A \trefi[functions]{function} of \trefi{arity} $k$ is called
\defi[name=nary]{$k$-ary}. For concrete $k$ we use \defi{unary} ($k=1$), \defi{binary}
($k=2$), and \defi{ternary} ($k=3$). An object $o$ can be thought of as a
\trefi[functions]{function} taking no \trefis[functions]{argument} and always
returning $o$. We speak of a \defi{nullary} function in this case. Finally, any
\mtrefi[?nary]{$n$-ary} function is called \defi{finitary}, if we do not want to
specify $n$.
\defi[name=nary]{$k$-ary}. For concrete $k$ we use \defi{unary} or
\defi[name=unary]{univariate} ($k=1$), \defi{binary} ($k=2$), and \defi{ternary}
($k=3$). An object $o$ can be thought of as a \trefi[functions]{function} taking no
\trefis[functions]{argument} and always returning $o$. We speak of a \defi{nullary}
function in this case. Finally, any \mtrefi[?nary]{$n$-ary} function is called
\defi{finitary}, if we do not want to specify $n$.
\end{definition}
\end{mhmodnl}
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