Definition:International Standard Book Number/ISBN-10
Definition
An International Standard Book Number is a codeword used to uniquely identify a published 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.
Examples
Example: $0$-$19$-$853453$-$1$
The book whose ISBN-$10$ code begins:
- $0$-$19$-$853453$
has a check digit of $1$.
Also known as
An International Standard Book Number is usually referred to by its abbreviation ISBN.
Also see
- Results about International Standard Book Numbers can be found here.
Linguistic Note
When referring to an International Standard Book Number by its abbreviation ISBN, beware not to vocalise it as "ISBN number".
The word number is already included in the abbreviation ISBN, so does not need to be repeated.
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes