Definition:International Standard Book Number/ISBN-10

Definition
An international standard book number is an index number used to uniquely identify a published.

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.