0.9999.... = 1.0

[allenmaher]

Jay520 said:

AbbathTheGrim said:
But the difference between 0.9999... and 1 is .1 not 0. 

Nope, it's zero. 

1 - 0.9 = 0.1

1 - 0.99 = 0.01

1 - 0.9999 = 0.0001

But when you have infinite nines, you also have infinite zeros and never reach the 1. 

  1.0000000000000000........
- 0.9999999999999999.........
=0.0000000000000000........

At no point will you ever reach ....0001.

Yes the number is for all practical purposes 1.  However by it infinately aproaches bet never reaches 1.  If you were to write the relationship you are still left with

1 > 0.99999999...

Much like limits at infinity that asymptotically aproach but never reach a value.