Okay…want to talk about the Book of Sand, only it seems the the wikipedia entry on it is really, really bad. So, look at it if you will, but don’t take it too seriously – the actual story is only a couple of pages long, so might be worth tracking down.
Anyway, so the book in the story has, it seems, an infinite number of pages whilst being of finite size. Other than the uncomfortable situation that Borges says that the pages are numbered.
He says that all the pages are numbered – that is to say that we have some division of the interval into a countable number of segments that, assuming homogeneity, are everywhere dense. These sorts of foliations leave me feeeeling queasy I have to say.
It is a suprisingly nontrivial to think of this mathematically – my initial reaction to it was due to a misthinking, that he was foliating the interval perfectly – that is to say that each page would be of zero thickness and correspond to a point on the interval – but then it would be impossible to number, well, (almost) any of them. This, whilst not being exactly what he meant, would link up well to another story, Odin’s Disk, where the chief artifact of concern was an infinitely thin disk (the translator calls it a circle, the only shape with exactly one side; I don’t know where these terminological/factual errors crept in).