Sheesh...I already had this argument...in school...ag it was annoying.
I will take that class eventually. So far I'm in geometry.
I think that both sides are correct in different manners. Even with infinite nines, when you think about it in pure logic, you never get to one. At the same time, .9 repeating is infinitely closer to one, so it becomes one.
My geometry teacher says that .9r <> 1. I'll just have to see a calc teacher...of course, Shvegait, having taken the class, can tell me.
In reality though, if you look around, is there anywhere that has a .9r in it anyway? I mean physically speaking. If you were to apply .9r to a thing, could it really exist since the nines would continue forever? Maybe...
I had a thought once, and it led me to the conclusion that, no math is really being done when something happens. For example, when you throw a ball. Math is not done to determine where it goes. It just is. So math seems to be more a translation of the laws of the universe into something we can manipulate and understand. In the reverse fashion, we can use math to predict how these laws apply also. Another thing I figured is that there is no such thing as a line. This is because a line is points. Points have no spacial value. The only reason we can see a line on a graph is because we give it width and height. Also, I don't think a physical straight line exists. The smallest existing unit of matter is round, as far as we know, and because of that is everything else not round also?
Math is wierd...
Note that everything above is simply past thoughts. I'm not trying to claim that what I've said is correct, although I do hope it is...
Go ahead and criticize stuff now... X|