.999999999(repeating) is equal to 1

I recognize that this has been fought over MANY times, and may be repetitive, but I feel it is a fascinating topic, and I'm eager to finish it. Now back to the debate: "However, the mathematician's side often fails to make the leap back to reality. " I would just quickly like to remind you, this debate has to do with mathematics, and not a concern with concepts of reality. Thus, the mathematician's side must be correct when judging the computation of a number. "You can't work with a number you can't specify, that's an extremely annoying situation. For this, there is the concept of infinity. Note the use of the word concept, because real infinity doesn't exist. (nothing is infinite, cause to take note of that - which is impossible too - you'd have to see it in its end state, if it's in an end state, you can technically get to the end, if it is still going on, you haven't achieved infinity, since you are at the very moment going further, so not in infinity)" So you agree that .999… is infinite, right? So as I represented earlier, through the equation, x=.999. .. <- .999… is represented as a variable. 10x=9.999. .. <- We multiply both sides by 10 to make the equation easier to understand. 10x-x=9.999. .. -.999. .. <- (*Note this) we have subtracted the ‘X' of the equation, which is an infinite decimal. Obviously, you know X-X must equal 0, so .999… -.999…. equals 0, in my representation, 9.999…-.999… must equal 9, and 10x-x must be 9x. ) x=1<-we divided both sides by 9 (9x=9), so 1 equals x .999. .. =1<- Plugging ‘x' in, we get 1=.999… Basically, in order to get my point across, I can subtract my concept of infinity by itself, and get 0, making the digit manipulation possible. You address that you have to "see" infinite in its end state. You can not "see" infinity. It is a mathematical term used to explain something that continues endlessly. Clearly, you can specify and infinite number in 2 simple examples, 1/3 and 2/3. 1/3=.333…. and 2/3=.666… the idea of infinity is clearly defined by a fraction, and can be multiplied by something to get a non-infinite decimal. (i. e. 1/3*3=1; .333…*3=1) either way, we have represented and infinite decimal and multiplied it by another number, receiving one whole number. *to sum this up, Infinity is endless, but can be specified by fractions. You can not "see" infinity, or "go" into infinity, simply because it's endless and has no "end state. " " So what is the practical concept based on - more or less - of infinity? Basically, on the fact that if you go that far, the difference doesn't matter. To give an example: if you write 1 instead of 0.9, you're making an error of the size of 0.1. Quite some people will still care you make such a rounding (depending on the situation ofc, but let's assume it does matter, for example the thickness of steel a car producer wants to order or so). If you write 1 instead of 0.99, you make an error of 0.01 and less people will make a fuss about the difference. Writing one 1 instead of 0.999 is only 0.001 off the mark. Even less people will care about such a tiny error. This would be true if the 9's stopped. Obviously, .999 is .999, not one; conversely, .999… is never ending and thus can not be justified by being a certain number less than one. To simplify this statement, I ask you, what is 1-.999…? It is a never ending series of zero's, with nowhere to verify a "1. " "Now this goes on and on, every step you go further the error gets smaller. At a certain point, the error is getting so extremely little that it really can be discarded for us, people. " If it's that tricky for "us, people," why not just round up? "Now one may try to argue that i'm making up how this concept is working. I'll give simple and - in a way - mathematical prove i'm not. For that, i'd like to make a practical example: the asymptote. Let's portray this 0.9999. .. as a function: y = 0.9*|_x_| (the |_ _| means you always round it down, no decimals) If you draw that, you'll get a horizontal asymptote y=1. " I believe you have made a major mistake. You can not multiply ‘x' by .9. You must multiply it by .999…, this is because .9 is equal to 9/10, 90%, etc. In other words, it stops, and is directly equal to .9. "Definition of an asymptote: "A linear asymptote is essentially a straight line to which a graphed curve becomes closer and closer but does not become identical. " -wikipedia And the same definition will be found in books on mathematics and i believe most people are familiar with asymptotes. A function never ever has a point in common with an asymptote, but always gets closer. That's an asymptote by definition. Yet if you'd take the limit of x to infinity, you get 1. If you say 0.999. .. is 1, you directly violate the definition and idea of an asymptote. So a mathematician has to admit that there is a distinction between reality and concept. Yes, you never touch it, so your y never is 1. But yes, we note it as one in the limit. Why? Because it is a workable concept: your calculations will still work out with this concept. " This doesn't work because your asymptote is incorrect. Sorry if I sound like an imbecile. XD - Btw i appreciate that you accepted such a difficult debate! ! Really! Sincerely, Julius Caesar