does 0.9999999.......... equal 1

You screwed up your maths dude! What you've written doesn't actually make any sense. There's no way multiplying a positive number greater than 1 by ten and then subtracting itself can produce a negative (and no, this isn't because my equation was wrong, you've just fallaciously extended a bastardised form of it's reasoning to the conceptual case of infinity). I think the problem is you have a fundamental misunderstanding of the nature of infinity. If you have an infinite number of nines in the positive direction that is just infinity. So your equation should read as follows: "(infinity)=x Multiply both sides by ten: 10(infinity)=10x We subtract the original x value from both sides and get: 0=10x-10(infinity) x=(infinity)" So this is saying x=(infinity) which is exactly what the first statement said, and your mathematical argument has been one big circle. The reason your mathematical reasoning fell apart is infinity doesn't always obey the same rules that standard numbers do. One can consider infinity to be more of a concept than a number. A lot of people have issues mathematically working with infinity because it is simply so incomprehensibly large that people fall into a number of reasoning traps, which if you go on to do higher level mathematics you might begin to understand the basis of. I can provide you with some other proofs if you'd like which show that 0.999...=1. I don't really want to have to type them out, so here's a link to some. (Please note it also includes the one I have already demonstrated). http://www.purplemath.com... I'd like to now spend a bit of time looking at some of the common reasoning flaws people fall into when they fail to realise 1=0.999... 1. It is common for people to assume that 0.999=/=1 because if you take 1-0.999... you will get 0.000...1. This is mathematically unsound as it demonstrates a misunderstanding of the nature of infinity. It is not possible to have an infinitely repeating decimal series followed by different digit because you will never reach that digit. There is an infinite number of zeros in the example 0.000...1, just as many zeros as there are in 0.000... As such it can be considered that you will never "reach" the 1 at the end of this infinitely many zeros. (I put reach in quotation marks because it is mathematically incorrect way of describing this scenario but it might make it easier to conceptualise for you). 2. Another common misconception that people make is they describe 0.999... as being similar to having an "asymptote" at 1, or getting infinitely close to, but never quite reaching 1. Again this is mathematically incorrect, and it displays a misunderstanding of both limit theorem, and the difference between a graph and a number. Numbers cannot express asymptotes. They do not "move" like a graph moves. They are at a fixed position on a number-line. If that position is anything less than 1, then there would theoretically be a number that was both greater than 0.999..., and less than 1. Such a number obviously does not exist. As such, there is no position besides the position of 1 on the number-line, that could be occupied by 0.999... without being mathematically incorrect. 3. A third misconception that is commonly made is people say 1-0.999... = 1/(infinity). This is produced again as a lack of mathematical understanding of the nature of infinity. "1/(infinity)=0" (by applying limit theory). In fact any non-infinite number when divided by infinity will be equal to zero. (Again I have taken a mathematical shortcut here, and infinity is more of a concept than a number, so we can't actually perform a simple operation like the one I just did, and instead you would need to apply limit theory to produce an answer, but based on your argument so far I don't think you would have covered mathematical limit theory yet, so I've used this shortcut to make it simpler for you. Although it's really interesting and I recommend you take a look at it on Khan Academy or something if you're not planning on studying it at university.). Here's the link to Khan Academy's series on limits and continuity if you'd like to take a look: https://www.khanacademy.org... I hope this has cleared things up for you.