This seems to be conflating 0.333…3 with 0.333… One is infinitesimally close to 1/3, the other is a decimal representation of 1/3. Indeed, if 1-0.999… resulted in anything other than 0, that would necessarily be a number with more significant digits than 0.999… which would mean that the … failed to be an infinite repetition.
Comment on I just cited myself.
ArchAengelus@lemmy.dbzer0.com 5 months agoIn this context, yes, because of the cancellation on the fractions when you recover.
1/3 x 3 = 1
I would say without the context, there is an infinitesimal difference. The approximation solution above essentially ignores the problem which is more of a functional flaw in base 10 than a real number theory issue
chaonaut@lemmy.world 5 months ago
Shampiss@sh.itjust.works 5 months ago
The context doesn’t make a difference
In base 10 --> 1/3 is 0.333…
In base 12 --> 1/3 is 3
But they’re both the same number.
Base 10 simply is not capable of displaying it in a concise format. We could say that this is a notation issue. No notation is perfect. Base 10 has some confusing implications
ColeSloth@discuss.tchncs.de 5 months ago
They’re different numbers. Base 10 isn’t perfect and can’t do everything just right, so you end up with irrational numbers that go on forever, sometimes.