And there's the rabbithole again...I spent much of last week being fascinated by reading around "Exact Real Arithmetic With Continued Fractions" (https://hal.inria.fr/inria-00075792/document, PDF). More resources on this on the Haskell wiki: https://wiki.haskell.org/Exact_real_arithmetic

...which is a bit mindblowing when so much of what we do uses numbers with limited precision. How can irrational numbers be represented in finite space? Using representations like this: http://en.wikipedia.org/wiki/Periodic_continued_fraction