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.

Perhaps I'm confused, but doesn't that site indicate that the midpoint of the positive rationals is 1.0? Or am I misreading it?

You are not misreading. That's correct.

But the article is saying that in Ruby, it's 1.5, right? So it's not the same as here? Or were you referring to the general notion of a midpoint of an infinite range?

Right again. The "also" is a reference to the parent comment.

> In surreal numbers [1], the midpoint between 0 and infinity would be the simplest number greater than 0, which is { 0 | } = 1

Oh, I see! For some reason I didn't spot the parent comment.