[gwern]

Borges's library can't contain itself because it is of a strictly finite size: the books are only 410 pages, or whatever, and so while astronomically large, the total number of sequences is finite. His point was that for any sub-book-sized claim, there would be another book contradicting it, if only through prefixing "it is not true that" or something.

His Book of Sand would, however, appear to be vulnerable to diagonalization.