0.9<overbar.> is literally equal to 1
There’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
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.
Even simpler: 1 = 3 * 1/3
1/3 =0.333333…
1/3 + 1/3 + 1/3 = 0.99999999… = 1
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.
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
