With so many people entering characters right now, it’s only a matter of time til we get some Shakespeare
That's the best thing I've read today. I've often heard the monkeys-on-typewriters imagery, but never related it to an idea of a "total library" which contains everything that can ever be written, probably even itself. I suppose the digits of Pi may be considered such a "library".
"Strictly speaking, one immortal monkey would suffice."
Here is the essay "Total Library" by Borges:
https://www.gwern.net/docs/borges/1939-borges-thetotallibrar... (PDF)
It mentions "abnormal transfinite numbers (whose parts are no smaller than the whole)". This seems to be a reference to Russell's Paradox:
https://en.wikipedia.org/wiki/Russell's_paradox
> Let us call a set "normal" if it is not a member of itself, and "abnormal" if it is a member of itself.
> Now we consider the set of all normal sets, R, and try to determine whether R is normal or abnormal. If R were normal, it would be contained in the set of all normal sets (itself), and therefore be abnormal; on the other hand if R were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal.
> This leads to the conclusion that R is neither normal nor abnormal: Russell's paradox.
That proves your point, that it's a mathematical impossibility.
Borges calls it "the vast, contradictory Library", so clearly he was aware of this fact.
His Book of Sand would, however, appear to be vulnerable to diagonalization.