0.999.../Proof by multiplication by 10

< 0.999...

AssumptionsEdit

ProofEdit


\begin{align}
x           &= 0.999\ldots \\
10 x       &= 9.999\ldots \\
10 x - x    &= 9.999\ldots - 0.999\ldots \\
9 x         &= 9 \\
x           &= 1
\end{align}