(December 13, 2015 at 5:07 pm)IATIA Wrote:
0.999... is valid
1 results in an indeterminate number.
The problem is basically apples and oranges.
![[Image: 0.999_1.png]](https://images.weserv.nl/?url=i285.photobucket.com%2Falbums%2Fll59%2FIATIA%2F0.999_1.png)
0.999... isn't valid in that formula.
Look at the denominator, 0.999... - 1. The result of that is going to be the difference between 0.999... and 1, correct? Well, what is the difference between 0.999... and 1? What must you add to 0.999... to get 1?
0.000...1? That's an invalid number. You can't have an infinite string of zeroes, and then a 1, at least not in regular math, because then the infinite string of zeroes isn't infinite, it's finite.
So the difference between 0.999... and 1 is 0, so the denominator is equal to 0, which means the formula results in an invalid number.
The problem isn't apples and oranges, it's apples and apples, because the two numbers have the exact same value. Unless you can show us that the denominator equals something else, you have no argument.
