Is there a surjective map between the (class of) ordinal numbers On and the set No (Conway's surreal numbers) and is it constructable, In Conway's system we have for example:
$\omega_0 = < 0,1,2,3,... | > $
$\epsilon = < 0 | 1, 1/2, 1/4, 1/8, ... > $
(where $\epsilon$ is not the first uncountable ordinal, but the "reciprocal" of $\omega_0$). My question is thus: can you device this for every ordinal, or does Conway's system On eventually run "out of space").