\begin{definition}[Definition:International Standard Book Number/ISBN-10]
An '''international standard book number''' is an index number used to uniquely identify a published {{WP|Book|book}}.
The '''ISBN-$10$''' format consists of a string of $9$ digits followed by a check digit in the set $\set {0, 1, \ldots, 9, X}$.
The check digit $d$ is calculated as follows.
Let $c$ be calculated as:
:$c = \ds \sum_{k \mathop = 1}^9 k d_k \pmod {11}$
where $d_k$ denotes the $k$th digit in the '''ISBN-$10$'''.
Then the check digit $d$ is defined as:
:$d = \begin {cases} c & : c \le 9 \\ X &: c = 10 \end {cases}$
Hyphens may be included in the string to separate out the sections for lexicographical convenience.
\end{definition}