This story ends with a footnote. That's right, a puny little footnote. But there's something you should know about footnotes in Borges' stories: they're a BIG deal. The thing is, we usually think of footnotes as little 'extra bits' to the main body of text – you know, stuff that wasn't important enough to make the cut, and got shoved off to the side.
Well, Borges likes to play with our preconceived notions about footnotes. See, he knows we're going to think the footnote is incidental. He knows we're going to try to skim over it without giving it much attention. So what does he do? He hides a HUGELY important idea in that tiny, tiny font, completely defying our expectations and changing the way we think about the entire text. And, once again, we might add, completely messing with our heads.
The final footnote, which describes a book of infinitely thin pages, blows our mind in two ways. First of all, it completely inverts the idea of the Library, forcing us to consider an infinity that expands inwards instead of outwards. And second of all, it contains the story's only mention of a female character – Letizia Alvarez de Toledo. And here we were thinking the universe was populated only by men.