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)
0.9<overbar.> is literally equal to 1
There’s a Real Analysis proof for it and everything.
Basically boils down to
That actually makes sense, thank you.
Even simpler: 1 = 3 * 1/3
1/3 =0.333333…
1/3 + 1/3 + 1/3 = 0.99999999… = 1
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.
ELI5
Mostly boils down to the pedantry of explaining why 1/3 = 0.(3) and what 0.(3) actually means.
0.9 is most definitely not equal to 1
Hence the overbar. Lemmy should support LaTeX for real though
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
Oh lol its rendering as HTML for you.