19hertz

ramblings of an electronic engineer.

0.999… = 1

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A recurring argument with one of my friends and myself is about a mathematical truth namely that 0.999… = 1. It’s an interesting concept which took me a while to grasp. To convince yourself have a look at these two proofs,

Proof 1 – Fraction Proof

1/9 = 0.111…

Multiplying both sides by 9,

9*(1/9) = 9*0.111…

9/9 = 0.999

1 = 0.999

Proof 2 – Algebra Proof

x = 0.999…

10x = 9.999…

subtracting x from both sides

10x – x = 9.999… – 0.999

9x = 9

x = 1

For more proofs check out the wikipedia entry.

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