Proof that 0.999... equals 1

Fraction proof
QED
 * 1) $$0.333... = \frac{1}{3}$$
 * 2) $$0.999... = 1$$ (multiply both sides by 3)

Algebra proof
QED
 * 1) $$x = 0.999...$$
 * 2) $$10x = 9.999...$$ (Multiply both sides by 10)
 * 3) $$10x - x = 9.999... - .999...$$ (Subtract x from both sides)
 * 4) $$9x = 9$$ (Simplify)
 * 5) $$x = 1$$ (Divide both sides by 9)