Definition:Factorial/Historical Note

From ProofWiki
Jump to navigation Jump to search

Definition

The symbol $!$ used on $\mathsf{Pr} \infty \mathsf{fWiki}$ for the factorial, which is now universal, was introduced by Christian Kramp in his $1808$ work Élémens d'arithmétique universelle.

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 Euler
$\mathop{\Pi} n$ as used by Gauss
$\left\lvert {\kern-1pt \underline n} \right.$ and $\left. {\underline n \kern-1pt} \right\rvert$, once popular in England and Italy.


Augustus De Morgan declared his reservations about 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.
-- 1929: Florian Cajori: A History of Mathematical Notations: Volume 2


The use of $n!$ for non-integer $n$ is uncommon, as the Gamma function tends to be used instead.


Sources