I think he just wrote it in a confusing way. The quote before says:

> (crucially, “to the left of all” and “to the right of all” also count as “gaps”)

So there are two "nothings" here, left of "all" - i.e. the zero - and right of it.

Though I'm not quite sure how you'd get infinite or irrational numbers by this procedure. Wouldn't you simply get the rational numbers by this?

(unless the "put a number" step is doing more work here than it seems. He doesn't really say which number to put there. In the examples, he mostly did "new number = (left number + right number) / 2", with special cases if any number is "nothing" - but he never actually wrote what the rules are here.)