Post by @SRAZKVT@tech.lgbt

2026-09-16 19:56 UTC

i find it wild how many people find issue with infinitely repeating decimals when a simple shift in perspective (or really, base) is enough to prove it's fine for example, don't understand why 0.99999... is equals to 1 ? that's because base 10 isn't able to properly represent thirds or ninths. if we were using base 3, a third is represented by 0.1, double it to get 0.2, add 0.1 again to get 1 it's just a problem of representation, the numbers are the same, the way we write numbers just isn't able to cope well with some of them (generally, any base will be unable to handle well any denominator it isn't a multiple of, which is why base 3 can't represent a half nicely)

Replies (2)

@SRAZKVT@tech.lgbt 2026-09-16 19:57

people always go and bring out the big guns of infinite series to prove it's fine when changing base is literally right there and free

Open ##4731997
@sodiboo@gaysex.cloud 2026-09-16 20:16

@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)

Open ##5318065