If you read the story you will see that most books present the appearance of random strings of characters.

If the sets of integers and reals is anything to go by, an infinitesimal portion of the books would include something that's actually legible, but perhaps the books could be sorted so those containing the most sensible arrangements of letters were kept nearby: don't bother looking at those noisy tomes of high entropy.

But perhaps the noise is just a language you haven’t recognized? Perhaps the noise contains True information when decoded using a scheme described in one of the other books?

O very true... you might start trying out one book as an XOR key to another. Of course, the result of decryption will already be sitting on the next shelf over :-)

Infinitesimal is a bit off, here. It's a very, very small but definitely finite proportion of books that'd be legible by humans in a human language.

You don't even need the full set of integers to catalogue the library, let alone the reals.

What I was trying to say was, since there are an infinite number of real numbers between each pair of integers, there would be a similarly infinite number of garbage text between each pair of legible texts.

Even though there are an infinite number of integers, there are an even more infinite number of reals, rendering the proportion of (integers)/(reals) to be near 0.

On the contrary, a random character string is meaningful in some conceivable language.

All you need is a reference to the book that describes the grammar of that language.

I'd say every set of whatever is a language. not the opposite tho