Quote (Hammer_Hdin @ Jul 9 2010 12:45am)
Here are a few concepts of infinity which might interest you:
1. Anything after an infinite series is ignored. Eg. 0.999... + 0.333... = 1.333... with a 2 at the end, but since the 2 is after an infinite series, the 2 is ignored.
2. Infinity minus 1 = infinity. Infinity plus 1 = infinity. Infinity - infinity does not necessarily equal 0.
3. Multiplication and division work both ways. For example, 1 divided by infinity cannot equal 0 because 0 multiplied by infinity is still 0, however the answer is infinitesimal (has a limit of 0).
There is absolutely no error in any of those concepts. It is not rounded, they are all exact.
Incase you are wondering what relevance that has to 0.999..., then we all know that 0.999... + 0.000... 1 = 1, right? Now the 1 is after an infinite amount of 0's. Therefore, it is ignored and changed into 0.999... + 0 = 1 which means that 0.999... must equal 1 (take away 0 from both sides of the equation). Another example was the 0.999... + 0.333... = 1.333...2 but since the 2 comes AFTER the infinite series, it is not included in the answer and there is no error whatsoever in ignoring it. A person was trying to argue that if you keep ignoring the number at the end of the infinite series then it will create an error factor which will eventually end up so large that it will change the outcome of the answer. That is wrong because whatever is after an infinite series will always remain after it and nothing will bring it back to the middle. Let's replace the last 1,000,000 digits in 0.999... with random numbers like 13582185. Since infinity minus 1,000,000 is still infinity, then there are still infinite digits of 9's before the random assortment of numbers, meaning that they are still ignored. I hope this explains something.
This isn't very accurate. You keep mentioning things being "after" an infinite series. This isn't possible (in R). This would imply the existence of infinitesimals, but infinitesimals are not real numbers. So when you say that .999... + 0.333... = 1.33...2, you're wrong. It just equals 1.333... You're also wrong when you say that .999... + .0...1 = 1 because .000...1 is not a real number.
NOTHING is ever "ignored." If it's there, it is significant. In this case, it's not there at all
