RE: If 0.999 (etc.) = 1, does 1 - 0.999 = 0?
March 4, 2012 at 6:08 pm
(This post was last modified: March 4, 2012 at 7:26 pm by Categories+Sheaves.)
There's a mountain of tacit assumptions being made when we write an infinite decimal. If you take a course in real analysis, you'll learn what that business is. But until then...
The main issue is that what you're thinking of when you write 1 - 0.999..., if this quantity isn't zero, is something that we can't represent with a decimal. I'm sure you've seen the "proof" about how 1/3 = 0.333... implies 1 = 3*(1/3) = 3*(0.333...) = 0.999...
That reasoning should be sufficient.
The main issue is that what you're thinking of when you write 1 - 0.999..., if this quantity isn't zero, is something that we can't represent with a decimal. I'm sure you've seen the "proof" about how 1/3 = 0.333... implies 1 = 3*(1/3) = 3*(0.333...) = 0.999...
That reasoning should be sufficient.
