"10X - X = 9X" is always true, not matter what X is, this is basic algebra.
X can be 43782487, and yet if you subtract one X from 10X, you still get 9X.
10X-X = 10*X- 1*X (1 is neutral element for multiplication, hence the identity) = (10-1)*X (distributive law) = 9*X
(10 - 1) * X = (9) * X
This works.
Ack. I've made a mistake.
(10 - 1) * X = (9) * X doesn't have anything to do with Mr. Col. Fishguts' proof up there.
It would have to be (10 - 1) * X = (9) + X.
9 * X /= 9 + X
If X = 0.999... = 1, then you'd get 9(1) = 9 + (1), and 9 /= 10.
Let me try again...
0.999... = 0.999... //multiply both sides by 10
9.999... = 9.999... //rewrite both sides
0.999...+0.999...+0.999...+0.999...+0.999...+0.999...+0.999...+0.999...+0.999...+0.999...=9+0.999...
//subtract 0.999... from both sides
9(0.999...) = 9 //divide both sides by 9
0.999... = 9/9 = 1 //identity property
0.999... = 1
Ohhh... Okay, I was wrong, Mr. Col. Fishguts. I misunderstood your proof. ^^;;
But the X = 0.999... bit was wholly unnecessary.
