Oscar Cunningham on Nostr: Given that hyperreals can be defined as equivalence classes of sequences of reals, ...

Given that hyperreals can be defined as equivalence classes of sequences of reals, you could say that 0.999… was notation for (0, 0.9, 0.99, …), which is indeed a hyperreal number less than 1. But I don't think this is a good idea, because there's not a good way to give every hyperreal a decimal expansion. Like, what would the square root of this number be?