0.9 is most definitely not equal to 1
Comment on I just cited myself.
LodeMike@lemmy.today 10 months ago
0.9<overbar.> is literally equal to 1
jonsnothere@beehaw.org 10 months ago
mathemachristian@lemm.ee 10 months ago
Hence the overbar. Lemmy should support LaTeX for real though
jonsnothere@beehaw.org 10 months ago
Oh, that’s not even showing as a missing character, to me it just looks like 0.9
At least we agree 0.99… = 1
LodeMike@lemmy.today 10 months ago
Oh lol its rendering as HTML for you.
UnderpantsWeevil@lemmy.world 10 months ago
There’s a Real Analysis proof for it and everything.
Basically boils down to
LodeMike@lemmy.today 10 months ago
Even simpler: 1 = 3 * 1/3
1/3 =0.333333…
1/3 + 1/3 + 1/3 = 0.99999999… = 1
UnderpantsWeevil@lemmy.world 10 months ago
But you’re just restating the premise here. You haven’t proven the two are equal.
This step
And this step
Aren’t well-defined. You’re relying on division short-hand rather than a real proof.
SuperSaiyanSwag@lemmy.zip 10 months ago
ELI5
Swedneck@discuss.tchncs.de 10 months ago
the explanation (not proof tbf) that actually satisfies my brain is that we’re dealing with infinite repeating digits here, which is what allows something that on the surface doesn’t make sense to actually be true.
UnderpantsWeevil@lemmy.world 10 months ago
Infinite repeating digits produce what is understood as a Limit. And Limits are fundamental to proof-based mathematics, when your goal is to demonstrate an infinite sum or series has a finite total.
beejboytyson@lemmy.world 10 months ago
That actually makes sense, thank you.