alt Hacker News> On the second day, there are two gaps: “between nothing and zero” and “between zero and nothing”. Two numbers spawn in those two gaps. Call them –1 and 1.
That's a mistake. They should've written "empty set of surreal numbers" and not "nothing".
It is a constructive theory, like sets/ordinals. For ordinals you can use ∅, { }, ∪ and you construct
∅, {∅}, {{∅},∅}, ... (von Neumann ordinals).
You build up surreal numbers as
{∅|∅}, {∅|{∅|∅}}, {{∅|∅}|∅}
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Edit: A happy accident: I denoted the "empty set of surreal numbers" with the symbol ∅. It works, and it gives you the surreal numbers. But if you think of ∅ as the empty set in set theory, then the same construction (using an ordered-pair construction) gives you the surreal numbers as sets!
What is the problem with saying “nothing” to mean “empty set” in an informal explanation? If you put apples between two bags, and the right bag is empty, it’s reasonable to say “nothing” accurately describes the contents of the right bag.
I’m slightly stretching the metaphor here because the number lines gives me enough structure (order expressed visually) and I only deal with at most one set item at a time (since we construct in the order of simplicity and can use the already constructed numbers), so it (IMO) unnecessarily complicates things to even talk about sets when we’re sort of just making cuts on the line. But in either case I don’t see the problem with colloquially saying “nothing” here.