Quote (Casey @ Jul 19 2010 11:12pm)
you people claiming .99999999999... will never get to 1 are totally missing how the decimal system works
when we say any number, such as 5.1429, that means 5(1) + 1(.1) + 4(.01) + 9(.001) + 0(.0001) + .....
.99999999... therefore, literally means the INFINTE sequence 9(.1) + 9(.01) + 9(.001) + 9(.0001) + .........
not a large number of nines after the decimal point; literally, infinite (countably infinite of course)
a fundamental property of real numbers is that any set bounded above has a LEAST upper bound, and that least upper bound (it's not hard to prove that it is unique) is a real number
all that remains is to show that the set: (9/10^n , n in the natural numbers) has least upper bound 1 (again, not hard)
no matter how you define the real numbers, .9999999..... = 1 (.9999999.... is not a mathematically rigorous definition, which is why many people naively assume it is not 1)
Sounds like this guy knows what he's talking about.