(March 4, 2012 at 6:08 pm)Categories+Sheaves Wrote: 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.
Yeah, that's true. Why does this necessarily need to be a problem though?
Quote: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.
Does 3.333* = 9.999* then? I know it comes out that way on the calulator but I thought that was just because we don't have room to write out the infinite 3's, nor is the caculator capbable of calculating infinity.
If that's true that makes sense then. I haven't come across that proof yet...the 9.999 = 1 thread was split up and I didn't read the first half of it. Or maybe I just skimmed over it in the other thread. Anywho, thanks for the clarification.
