0.99999...=?

Hi anonymous,

Good thinking but your logic is a little floored because there are an infinite number of 0s before the 1.  

So the 1 is never reached.

$$\\\frac{1}{3}=0.33333333.......\\\\ \frac{2}{3}= 0.66666666........\\\\ \frac{3}{3}=0.999999999....... = 1$$

0.9 repeater equals 1

but 1- 0.9999999999...=o.ooooooooooooooooooooooooo1

and since 0.00000000000000001 does not = 0

0.999999999999999 does not = 1

Look at it this way:

Let        x = 0.9999999999.....

Then  10x = 9.9999999999...

Subtract the first from the second to get

10x - x = 9.999999999.... - 0.999999999...  

or 9x = 9

so x = 1