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Does 0.999… = 1?

Using fractions:

1/9 = 0.111…

9 x 1/9 = 9 x 0.111…

1 = 0.999…

 

Using algebra:

    x   =   0.999…

10x   =   9.999…

         =  9 + 0.999…

         =  9 + x

  9x    =  9

    x    =  1