0.999.../Proof by multiplication by 10

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Assumptions[edit]

Proof[edit]


\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}