So the surreal numbers aren't totally ordered
under earliness, they're only partially ordered.
A concept that Kruskal
calls earliness is what makes such definitions possible.
This is not to say that
earliness is all - important.
In this case, that's by exploiting the Labour implosion,
the earliness of the Lib Dem recovery and the turmoil and uncertainty of Brexit before its impossibility becomes yet more obvious.
This property makes it possible for mathematicians to use
the earliness ordering to find definitions and proofs and carry out other vital mathematical activities, relying on a method called transfinite induction.
The earliness ordering has another important quality: every nonempty class of numbers has at least one earliest number (remember, not all numbers in a class can be compared for earliness — two or more numbers could be the earliest in the class).
The fact of
its earliness, I've learned, will be proved by an imperceptible difference in taillight size and a few other things too dull to recount.
It's not about
the earliness of the hour.