An International Standard Book Number is not always assigned.
 (These proofs are true because the ISBN is less than eleven digits long and because 11 is a prime number
=== ISBN-10 check digits ===According to the 2001 edition of the International ISBN Agency's official user manual, the ISBN-10 check digit (which is the last digit of the 10-digit ISBN) must range from 0 to 10 (the symbol 'X' is used for 10), and must be such that the sum of the ten digits, each multiplied by its (integer) weight, descending from 10 to 1, is a multiple of 11

