0.999...=1/Proof 2
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Theorem
- $0.999 \ldots = 1$
Proof
| \(\displaystyle 0.333 \ldots\) | \(=\) | \(\displaystyle 1 / 3\) | |||||||||||
| \(\displaystyle \leadsto \ \ \) | \(\displaystyle 3 \paren {0.333 \ldots}\) | \(=\) | \(\displaystyle 3 \paren {1 / 3}\) | ||||||||||
| \(\displaystyle \leadsto \ \ \) | \(\displaystyle 0.999 \ldots\) | \(=\) | \(\displaystyle 3 / 3\) | ||||||||||
| \(\displaystyle \) | \(=\) | \(\displaystyle 1\) |
$\blacksquare$
