@SRAZKVT@tech.lgbt the way i see it is that changing base only helps me convince myself that maybe 1/3 ≠ 0.33333… because, yes, indeed, in another base, the finite representations add nicely. but in decimal, clearly "1.0" and "0.99999…" are not the exact same sequence of symbols, and if they're not equal, it follows that "0.33333…" is a third of "0.99999…", not a third of "1.0". so if i take it at face value that decimal just can't cope with a third, then I'd be ready to accept that maybe it can't write a third. and indeed, it seems a uniquely decimal problem, because as you say, in base 3 there just Isn't this ambiguity. (and if i do accept that 0.3333… is a third of 1.0, then i think a much easier proof is that multiplying by three gives 0.9999… and 1.0 at the same time; thus those are equal)