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Jorge Luis Borges’ haunting short story The Library of Babel introduces a compelling concept: the Total Library. By “total” is meant that it contains every possible book, at least up to a certain length. In Borges’ story, the books each have 410 pages, and on each page are 40 lines and 80 columns. Also, there are only 25 characters altogether, including the space. The multiplication principle shows us that there are therefore 410 × 40 × 80 = 1,312,000 positions for characters in each book, and since there are 25 possible characters we get 25 raised to the 1,312,000th power as the total number of books in Borges’ total library. (This number is unimaginably huge – but it is still finite.)



As Borges tells us, since it contains every book, the library contains “everything: the minutely detailed history of the future, the archangel’s autobiographies, the faithful catalogue of the Library, thousands and thousands of false catalogues, the demonstration of the fallacy of those catalogues, the demonstration of the fallacy of the true catalogue, the Gnostic gospel of Basilides, the commentary on that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book in all languages, the interpolations of every book in all books.” Of course, it contains mostly nonsense. For instance, one of the books is just solid b’s, except for the 4,213th character, which is a q. (I personally take pleasure in knowing that there is a copy of Mark Twain's Tom Sawyer, faithful but for the fact that Tom is called “Silly Putty.”)
Today's challenge: Does the Total Library contain a complete account of all of mathematics? (Would it make any difference, since the books are limited to 410 pages, if we allowed multi-volume works, up to any finite number of volumes?)

MISLEADING HINT


Solution to yesterday's challenge



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