0.9999.... = 1.0

[Jay520]

KylieDog said:

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.

At no point will that 0.9999 ever become 1 either.

If you accept that there are infinite 9s then it is. 

Just like the fraction 5/7 doesn't equal 0.714285.... or 0.714285714285, but it does equal the the repeating decimal 0.714285 (with an infinite number of 714285s).