0.9999.... = 1.0

[dsgrue3]

Jay520 said:

This is a fairly old topic so I'm not sure if all of you have heard about this. I just found out about it and found it interesting.

The claim is that 0.9999.....(infinite 9s) is equal to 1.

Here are some proofs

-

x = 0.9999…	given
10x = 9.9999….	multiply by 10
9x = 9	subtract x
x = 1	divide by 9
0.999... = 1	substitution

 

You went from 10x = 9.9999... and by subtracting x somehow arrived on 9x = 9; this is wrong. You should have arrived on 9.000.....1x = 9.

Series will converge to 1, but never arrive at it. It's like saying that you can divide 1 in half and eventually get to 0. You can't. You can approach 0, but never reach it. 

As to 1+1 =3 for sufficiently large values of 1, it's just a joke. 1.49 +1.49 = 2.98.