Exactly what I came to post. This is an important model for numbers. Traditionally one distinguishes between rational, algebraic, and transcendental numbers; e

Exactly what I came to post. This is an important model for numbers. Traditionally one distinguishes between rational, algebraic, and transcendental numbers; e is transcendental. This tree is related to continued fraction expansions. Any number is a limit of a path in this tree, and one can talk about the pattern in the path from a CS automata theory point of view. Now e comes out one of the easier limits.