birthdays
Start at day 0 with 0 = { | }. Each new day inserts the simplest missing dyadic fractions between older numbers.
Surreal numbers are born from cuts { left | right }. Every left option must be smaller than every right option; the number created is the simplest value between them.
try these
why it is nice
With one recursive rule, surreals contain integers, fractions, real numbers, infinities like ω = { 0, 1, 2, ... | }, and infinitesimals like 1/ω. The finite part shown here is already a tiny universe: numbers appear when there is room for them to be the simplest choice.