Even simpler: 1 = 3 * 1/3
1/3 =0.333333…
1/3 + 1/3 + 1/3 = 0.99999999… = 1
Comment on I just cited myself.
UnderpantsWeevil@lemmy.world 6 days agoThere’s a Real Analysis proof for it and everything.
Basically boils down to
- If 0.(9) != 1 then there must be some value between 0.(9) and 1.
- We know such a number cannot exist, because for any given discrete value (say 0.999…9) there is a number (0.999…99) that is between that discrete value and 0.(9)
- Therefore, no value exists between 0.(9) and 1.
- So 0.(9) = 1
LodeMike@lemmy.today 6 days ago
UnderpantsWeevil@lemmy.world 6 days ago
Even simpler
0.99999999… = 1
But you’re just restating the premise here. You haven’t proven the two are equal.
1/3 =0.333333…
This step
1/3 + 1/3 + 1/3 = 0.99999999…
And this step
Aren’t well-defined. You’re relying on division short-hand rather than a real proof.
SuperSaiyanSwag@lemmy.zip 5 days ago
ELI5
UnderpantsWeevil@lemmy.world 5 days ago
Mostly boils down to the pedantry of explaining why 1/3 = 0.(3) and what 0.(3) actually means.
beejboytyson@lemmy.world 5 days ago
That actually makes sense, thank you.
Swedneck@discuss.tchncs.de 3 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 3 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.