You don't even have to assume the alphabet is finite, merely countable, and you still have exactly one book for each finite string of bits. In other words, the

You don't even have to assume the alphabet is finite, merely countable, and you still have exactly one book for each finite string of bits. In other words, the set of every finite sequence of integers (or natural numbers, rationals, finite strings of Chinese characters, etc.) is no larger than the proper subset of "every sequence of length one". A library with uncountably many distinct volumes is a fun thought experiment, though, as is a text written in a language that uses an uncountable alphabet, wherein a single letter potentially contains an infinite amount of information...