0.9 is most definitely not equal to 1
Comment on I just cited myself.
LodeMike@lemmy.today 1 week ago
0.9<overbar.> is literally equal to 1
jonsnothere@beehaw.org 1 week ago
mathemachristian@lemm.ee 1 week ago
Hence the overbar. Lemmy should support LaTeX for real though
jonsnothere@beehaw.org 1 week 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 1 week ago
Oh lol its rendering as HTML for you.
UnderpantsWeevil@lemmy.world 1 week ago
There’s a Real Analysis proof for it and everything.
Basically boils down to
LodeMike@lemmy.today 1 week ago
Even simpler: 1 = 3 * 1/3
1/3 =0.333333…
1/3 + 1/3 + 1/3 = 0.99999999… = 1
UnderpantsWeevil@lemmy.world 1 week 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 1 week ago
ELI5
Swedneck@discuss.tchncs.de 5 days 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 5 days 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 1 week ago
That actually makes sense, thank you.