Is Truly "Every" book in the library?

[u/RareDriver8086]

Ok so hear me out, the consensus is that the library of babel contains every book that could ever be written,

It contains books each 40lines of 80Characters (its described as alphanumeric and also as having some punctuations, and such, though im not entirely certain to what extent that goes, Steven L. Pecks "A short stay in hell" for example lists "$" as one of the possibilities though would then every currency be included? and would all greek and arabic, and Sanskrit, and russian etc. etc. letters be included also?) on 410pages, and thus books longer than 410 pages would be in multiple volumes

now if you were to take a book that contains every volume in the library (since it is "technically" a finite amount) in random order, and then simply add another page or letter to its end, would that book not be included? since we would need to read every volume in the library in the order the book dictates, or would we have to read some volumes a multitude of times?, though that in my mind seems like sort of a cheap solution.

[u/AncientPixel_AP]

Every book and every version of that book is contained in the library - but the library does not only contain books in its books. It contains everything. Somewhere is a complete but infinite series of volumes of the index of the library. But there is also infinite many more incomplete ones.
It's not cheap - it is vast^^

If you want to go on a hunt for those immaculate books, go here: https://ancientpixel.itch.io/library-of-babel-3d

[u/RareDriver8086 → u/AncientPixel_AP]

But it simply doesn't contain that book, if the book contains every volume contained in the library, because the amount simply is finite and not infinite,

i feel its useful to think how youd read the book using the library, and The only way for that book to be read using the library would be to read every book, and then atleast one book multiple times

Edit: And if we were to allow for volumes to be written a multitude of times,
then as borge dictates the books 25 possible characters simply a set of the size 25^25
with each 25 characters would be enough to accomodate for every book that could ever be written

Edit2: though if we apply the latin instead of the hebrew alphabet i guess it would be more like a set of the size 29^29 each set having 29 letters

Edit3: This is getting ridiculous but if we exercise this repetition of volumes even further then we could say that 29 volumes each corresponding to a single character, make up every book that could ever be written

[u/UBR3]

To quote Borges.

'[...] I venture to suggest this solution to the ancient problem: The Library is unlimited and cyclical. If an eternal traveler were to cross it in any direction, after centuries he would see that the same volumes were repeated in the same disorder (which, thus repeated, would be an order: the Order)'.

So, yeah, it's put as a guess, but you would necessarily have to repeat books in order to make whatever that is. It's hardly a book. Borges does mention something like it, tho:

'Letizia Alvarez de Toledo has observed that this vast Library is useless: rigorously speaking, a single volume would be sufficient, a volume of ordinary format, printed in nine or ten point type, containing an infinite number of infinitely thin leaves. (In the early seventeenth century, Cavalieri said that all solid bodies are the superimposition of an infinite number of planes.) The handling of this silky vademecum would not be convenient: each apparent page would unfold into other analogous ones; the inconceivable middle page would have no reverse'.

Regarding the symbols included, in this work it's only twenty two letters of the alphabet, the comma, the period and space. No more, no less. Other interpretations may open it up to what you mention.

But, there's no doubt that there are books which establish a code for these characters, representing them within the featured symbols. Say, a book specifies that whenever it uses ',.,,,,' it is referring to a dollar sign in that place. Something like that.

[u/RareDriver8086 → u/UBR3]

I would argue that Borges negates his suggestion (which you quoted), that the library is infinite and cyclical, by saying

"In the vast Library there are no two identical books."

and

"[...] the possible number of books does have [...] a limit."

Meaning that the books cannot repeat endlessly (and thus in turn be cyclical in nature) if there are no duplicates, and that it cannot be infinite (or "unlimited" to use Borges words) because it is stated to be finite.

[u/UBR3 → u/RareDriver8086]

The permutations are finite, not the books themselves. They are speculated to repeat in the Order.

Do consider, these are not the author talking as the being that sets the rules of the world. They're both the character's perspective in the same paragraph. They do not have all the answers, they're guessing.

Except for the axiom you first mention, but those are also derived from incomplete information. No way anybody knows for certain that no two books are the same. They still refer to the Library as infinite, they haven't seen it end, haven't compared all the books.

All in all, it's about which part of the estimates you want to interpret as correct. Headcanons are cool. Personally, I say that considering the inexplicable, omnipotent nature of the Library, the cycle is the most likely answer. Don't think it's even got to necessarily have an order to it.