firstname.lastname@example.org: Surreal numbers might not have a decimal expansion all their own, that no other surreal number has as the nearest value, but, any surreal number between negative infinity and infinity (and there are others) can be mapped to exactly one decimal expansion, and, furthermore, with that d(s1) < d(s2) => s1 < s2.
Hmm. omega-1 is less than infinity, being one larger than omega-2. How would you denote that decimal expansion of (1/(omega-1)) and (1/(omega-2)) has the desired properties, without going into things disagreeing with the topic "Do you think that 0.000...1 is any less sound a concept than 0.999... ? YES!), given that both decimal forms go 0.000...something.