It’s definitions/conventions all the way down. Which particular construction/definition of “the” reals/hyper reals are you referring to? The expansion of the

It’s definitions/conventions all the way down. Which particular construction/definition of “the” reals/hyper reals are you referring to? The expansion of the “0.n…” notation is a separate matter. It also depends on which particular definition of “=“ and “!=“ you are using. x != y could be the classical “not(x = y)”; or the constructive “x < y OR y < x”. So if 0.999… < 1 is an error, is it a syntax or semantic error? https://en.wikipedia.org/wiki/Construction_of_the_real_numbers https://en.wikipedia.org/wiki/Construction_of_the_real_numbe...