3 ms·

It's also the midpoint of the positive rationals, as modeled by the Stern-Brocot tree. https://www.cut-the-knot.org/blue/Stern.shtml https://www.cut-the-knot.o

It's also the midpoint of the positive rationals, as modeled by the Stern-Brocot tree. https://www.cut-the-knot.org/blue/Stern.shtml https://www.cut-the-knot.org/blue/Stern.shtml

Syzygies 6y ago
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.
Jweb_Guru 6y ago
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?
- recursive 6y ago
  You are not misreading. That's correct.
  - Jweb_Guru 6y ago
    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?
    - recursive 6y ago
      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
      - Jweb_Guru 6y ago
        Oh, I see! For some reason I didn't spot the parent comment.