Simple, Elegant Proof of 0.999… = 1 Camino, Mhd Abstract: Today I prove 0.999… = 1. This has been done before, but for some reason /sci/ still doesn’t agree. So today I am going to use a proof that is so simple that it doesn’t even involve calculus, geometric series, or even multiplication. This proof came to me in a dream, and when I awoke I quickly scribbled it down on a piece of paper.
S = 0.9999… Add 0.1111… to both sides to get: S + 0.1111… = 0.9999… + 0.1111… Look at the right side of the equation. 0.9999… + 0.1111… = 0.9 + 0.09 + 0.009 + … + 0.1 + 0.01 + 0.001 + … = (0.9 + 0.1) + (0.09 + 0.01) + (0.009 + 0.001) + … = (1) + (0.1) + (0.01) + (0.001) + … = 1.11111… Okay! So now we have: S + 0.1111… = 1.1111… Now subtract 0.1111… from both sides: S = 1 Sub for S: 0.9999… = 1
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