'The Library of Babel' - Jorge Luis Borges:

'The Library of Babel' - Jorge Luis Borges:

>I have just written the word “infinite”.' I have not interpolated this adjective out
of rhetorical habit; I say that it is not illogical to think that the world is infinite.
Those who judge it to be limited postulate that in remote places the corridors and
stairways and hexagons can conceivably come to an end--which is absurd.
Those who imagine it to be without limit forget that the possible number of books
does have such a limit.

Does it really, though? How can the number of books in the Library be finite if the possible combinations of letters can always be increased by adding more letters, words, and pages, ad infinitum.

At some point the books won't fit on the shelves anymore

The books are all exactly 401 pages, which leads me to believe that they're all split up into different volumes.

410* pages, sorry

If they're all exactly 410 pages, and let's say a page fits 500 letters, and a letter can only be chosen from the alphabet, then you can have only 500*410*26 combinations

yes: it's finite
nope: a little bit more than that

No, that's not how it works. The Library contains every single book that can possibly exist in the universe (including the book that is the perfect compendium of all other books in the Library). In other words, it contains every possible combination of the 23 letters. Each volume is 410 pages, but there obviously are a lot of books that exceed this limit, so I assume they're broken up into many different volumes (like, for instance, Infinite Jest Vol I, II, and so on).

The problem is that there can be no limit to the number of letters or words or paragraphs or even pages in a book. This, of course, means that the books must be as infinite as the Library, contrary to what Borges says.

>The problem is that there can be no limit to the number of letters or words or paragraphs or even pages in a book
The story specifically says that every tome has a set amount of pages.

>there are rules!!!
>but there are no rules!!!!!

well if the rules don't count then it can be infinite, then there can be a whole section where all books have been tattooed on the eye-lids of African ex-prostitute hippos

++
going with your estimation of 410 pages & 500 letters per page, you can have 26^(500*410) different books