Proving 0.999... Is Equal To 1

eldavojohn writes "Some of the juiciest parts of mathematics are the really simple statements that cause one to immediately pause and exclaim 'that can't be right!' But a recent 28 page paper in The Montana Mathematics Enthusiast (PDF) spends a great deal of time fielding questions by researchers who have explored this in depth and this seemingly impossibility is further explored in a brief history by Dev Gualtieri who presents the digit manipulation proof: Let a = 0.999... then we can multiply both sides by ten yielding 10a = 9.999... then subtracting a (which is 0.999...) from both sides we get 10a — a = 9.999... — 0.999... which reduces to 9a = 9 and thus a = 1. Mathematicians as far back as Euler have used various means to prove 0.999... = 1."

Comments

Camel's Nose

[DumbSwede]

3D may not be being adopted has quickly as TV manufactures would like, but I don't think it is going away. This isn't the same once every decade or so gimmick it was. But the camel's nose under the tent won't be movies I think, but rather immersive 3D games with good 3D tracking.

I haven't yet tried Sony's Move system, but couple 3D tracking with a large 3D display and you may have an unbeatable gaming experience. I am also not a Second Lifer or a WoW player, but again 3D seems ideal for when you are not just looking passively at a story being told, but must move about in an environment. 3D Desktops have been predicted for quite sometime, but perhaps you really need true 3D to pull of a 3D Desktop.

Still this may all fall to wayside if someone can get rid of the screen, giving you true mobility in a 3D space. Yes there are VR 3D headsets, but they are clunker than the 3D glasses everyone here is already complaining about and high definition VR headsets are prohibitively expensive. No doubt technology will eventually catch up with how to make a high definition, light weight, untethered, long battery life, unobtrusive, VR headset.

On a related note, more than 3D for passive content, we need higher frame rates. There seems to be some conception that movies must be in 24fps to have a 'movie' feel as opposed to a 'TV' feel. I don't know any TV in full progressive 60fps. Most prime time TV shows are shot on 24fps film. 60fps 1080p would be much more immersive for high motion scenes. Someone needs to shoot some action epic in 60fps or higher and see if the public responds to it. IMAX once sometime ago shot one or two films in 48fps. It was insanely expensive to pull off back then, but now should be a cinch. Oddly almost every one's HDTV is capable of displaying 60fps, but unless you are using it for gaming it probably never use more than half this bandwidth.

But why do numbers like this go infinite?

[Xaedalus]

Pi for instance. As far as I can tell, it's infinite. Or 1/3 translating to 0.33333 et al. Why do these numbers go infinite? Why isn't there a definite end? And, what are the real world implications of an infinite number?

Re:(0.999...)st Post!

[SpryGuy]

Hey! He said "Maths is fun", not grammar!