\begin{definition}[Definition:Divisor (Algebra)/Notation]
The conventional notation for '''$x$ is a divisor of $y$''' is "$x \mid y$", but there is a growing trend to follow the notation "$x \divides y$", as espoused by {{AuthorRef|Donald Ervin Knuth|Knuth}} etc.
From {{BookReference|Concrete Mathematics: A Foundation for Computer Science||Ronald L. Graham|author2 = Donald E. Knuth|author3 = Oren Patashnik|ed = 2nd|edpage = Second Edition}}:
:''The notation '$m \mid n$' is actually much more common than '$m \divides n$' in current mathematics literature. But vertical lines are overused -- for absolute values, set delimiters, conditional probabilities, etc. -- and backward slashes are underused. Moreover, '$m \divides n$' gives an impression that $m$ is the denominator of an implied ratio. So we shall boldly let our divisibility symbol lean leftward.''
An unfortunate unwelcome side-effect of this notational convention is that to indicate non-divisibility, the conventional technique of implementing $/$ through the notation looks awkward with $\divides$, so $\not \! \backslash$ is eschewed in favour of $\nmid$.
Some sources use $\ \vert \mkern -10mu {\raise 3pt -} \ $ or similar to denote non-divisibility.
Category:Definitions/Divisors
\end{definition}