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ISBN-13 is checked in check_isbn(). If the number is valid the result will be 0. Before calling this function, ...
It can be proven mathematically that all pairs of valid ISBN-10s differ in at least two digits. It can also be proven that there are no pairs of valid ISBN-10s with eight identical digits and two transposed digits (these proofs are true because the ISBN is less than eleven digits long and because 11 is a prime number). The ISBN check digit ...
ISBN-13 is checked in check_isbn(). If the number is valid the result will be 0. Before calling this function, ...
The final digit of a Universal Product Code, International Article Number, Global Location Number or Global Trade Item Number is a check digit computed as follows: [3] [4]. Add the digits in the odd-numbered positions from the left (first, third, fifth, etc.—not including the check digit) together and multiply by three.
calling functions are required to ensure that <isbn13> is a properly formed string of 13 digits (no separators) that begins with 978.]] local function convert_to_isbn10 (isbn13) local isbn9 = isbn13: sub (4, 12);-- get the 9 digits of <isbn13> that follow the '978' GS1 prefix (drop the check digit) local check = 0;-- initialize the check digit ...
The check digit is there to check whether the main part of the number is correct. If the ISBN is failing to validate, it is likely that there is a typo in the main part of the number. In this case, recalculating the check digit results in an apparently valid ISBN that leads to the wrong source (or to nowhere).
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ISBNs only identify a particular edition of a book, and a reader with only an ISBN will not see the full range of versions of the book. Please do not use ISBNs alone to identify books: add a proper citation as well as the ISBN. Also note that ISBNs are not required of citations; popular citation styles like Chicago, MLA, and APA do not