Subscribe!Here's a video I made in the wee hours while in the lab last night. It explores the question of whether or not 1 = 0.999..., where there are an infinite number of 9s following the decimal point, by demonstrating three proofs.
Does 1 = 0.999. . .? - video powered by Metacafe
As to whether you accept the proof depends your intuition and beliefs about real numbers. Can you operate on integers the same way you operation on fractions? This problem arises from applying mathematical operations to an infinite series (0.999 = 9/10 + 9/100 + 9/1000 . . .). The best counter argument I've heard against the demonstrated proofs is that there should be an infinite number of points between 0.999... and 1. The debate is by no means settled, and as a amateur mathematician I certainly can't provide much more insight than I already have.
