0.9999999 = 1

10x - x = (10 - 1)x = 9x

if x = 0.99..., then 9x = (9)(0.99...) != 9


This whole thing revolves around fiddling with invalid operations.

a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1

It's like dividing by 0 and then "proving" that 1 = 2.

your proof that 2=1 is invalid since if a = b, then a-b = 0 and the whole thing becomes 0; you'd also need to divide by 0 in the 4th line, which isn't valid. The proof that 0.99...=1 doesn't divide by 0.

err, didn't see this thread was locked.