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