\begin{definition}[Definition:Factorial/Historical Note]
The symbol $!$ used on {{ProofWiki}} for the factorial, which is now universal, was introduced by {{AuthorRef|Christian Kramp}} in his $1808$ work {{BookLink|Élémens d'arithmétique universelle|C. Kramp}}.
Before that, various symbols were used whose existence is now of less importance.
Notations for $n!$ in history include the following:
:$\sqbrk n$ as used by {{AuthorRef|Leonhard Paul Euler|Euler}}
:$\mathop{\Pi} n$ as used by {{AuthorRef|Carl Friedrich Gauss|Gauss}}
:$\left\lvert {\kern-1pt \underline n} \right.$ and $\left. {\underline n \kern-1pt} \right\rvert$, once popular in England and Italy.
In fact, {{AuthorRef|Henry Ernest Dudeney}} was using $\left\lvert {\kern-1pt \underline n} \right.$ as recently as the $1920$s.
{{AuthorRef|Augustus De Morgan}} declared his reservations about {{AuthorRef|Christian Kramp|Kramp}}'s notation thus:
:''Amongst the worst barbarisms is that of introducing symbols which are quite new in mathematical, but perfectly understood in common, language. Writers have borrowed from the Germans the abbreviation $n!$ ... which gives their pages the appearance of expressing admiration  that $2$, $3$, $4$, etc., should be found in mathematical results.''
::::-- {{BookReference|A History of Mathematical Notations|1929|Florian Cajori|volume = 2}}
The use of $n!$ for non-integer $n$ is uncommon, as the Gamma function tends to be used instead.
\end{definition}