alt Hacker NewsThank you for writing a detailed explanation! I've slightly edited mine to explain the infinity jump. Yours is, of course, much more detailed.
For the infinitesimal number, I think it makes more sense to use {0}|{1,1/2,1/4,1/8,...} since it gets born at the same day as say 1/3. So it is easier to understand how it arises without "waiting" for all reals.
Oops, that was an oversight: indeed you don't get all the rationals I need for what I wrote until "one day later" (in Knuth's terminology). Regrettably I'm too late to edit what I wrote above.