10X-X= 9x Except x= .999..... So .9999x9=8.99 so 9X= 8.999... And even though 9.999-.999 is true, you cannot say 9X=9 and 9X=8.999, you multiply the variable by the number of times necessary (9) and get 9X= 8.999, so there is no way that 9X=9. Therefore .999... Doesn't equal 1.
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Edited by kgj: 7/13/2013 11:37:05 PM[quote] you cannot say 9X=9 and 9X=8.999,[/quote] Let 9X=9 be equation 1 and 9X=8.999... be equation 2 8.999...=9X 90X = 89.999... 90X-9X=89.999...-8.999... 81X=81 X=1 Substituting X into equation 2: 9X=9 9(1)=9 9=9 So the identity is true. Cool.
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If you accept that X = 0.999... and 10X = 9.999... then you must accept that 9X = 9 as a mathematical fact. We cannot arbitrarily choose what 9X equals, it equals precisely 9 if we wish to be mathematically sound.
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It does equal 9. And it's proven by the very fact that 0.9... is equal to 1.