0.9999.... = 1.0

[BlkPaladin]

dsgrue3 said:

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.

Once you add percision to that. He using a percison of 1., which technically will not work either. Because you usually round to the percision before adding anyways. I got into an argument with a friend of mine about this. Yes you can do it the way he wants to and end up with 3. But it not proper technique, with Percision and Accuracy both going out the window. The correct technique is the way you did it.