Quote Originally Posted by Arche
How does it show why 1.9 != 2? You can show it algebraically.

1.9 = 1 + 0.9

Let 0.9 = X, then

10X = 9.9
9X = 9.9 - 0.9 = 9
X = 1

We know 1.9 = 1 + 0.9, so

1.9 = 1 + X = 1 + 1 = 2
Doesn't this algebraic proof rely on multiplying the infinite decimals, which can't really be done?