0.999...=1/Proof 4

Theorem

 * $0.999 \ldots = 1$

Proof
We begin with the knowledge that:

Now we divide $9$ by $9$ using the standard process of long division, only instead of stating that $90$ divided by $9$ is $10$, we say that it is "$9$ remainder $9$," yielding the following result: 0.9999...   ---   9|9.0000...     8.1     ---       90       81       --        90        81        --         9...

Thus, we are compelled to believe that:
 * $0.999\ldots = \dfrac 9 9 = 1$