0.999.../Proof by multiplication by 10

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Assumptions

Proof

\begin{matrix} x & = 0.999 \dots \\ 10 x & = 9.999 \dots \\ 10 x - x & = 9.999 \dots - 0.999 \dots \\ 9 x & = 9 \\ x & = 1.000 \dots \end{matrix}

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