1 = 0.999999... Proof: Let x = 0.999999... <-----------------------| | 10x = 9.999999... Mult. both sides by 10 | -x = -0.999999... Subtract 1x from 10x | ------------------- | 9x = 9.000000... | | x = 1 Divide both sides by 9 | to solve for x. | Substituting for x above --------------------| 1 = 0.999999... Freaky!