.999999999(repeating) is equal to 1

This is probably one of the hardest fought debates imaginable. It is my sincere belief that is due to both parties failing to make distinction between 'reality' and mathematics. The mathematical proof given is a 100% correct and trying to argue against it is a lost fight, but still people keep trying. You can't beat mathematical proof. If it's proven, it's correct, no matter what you try. However, the mathematician's side often fails to make the leap back to reality. If you keep on placing 9's, it doesn't turn in a 1. You can keep adding 9's all your life, make your children do it and their children and so on (and even then you don't achieve infinity), it won't make it one. What number is it? Impossible to tell, nobody can tell. Now, back to mathematics. 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) The mind isn't even capable of grasping with it, let alone working with it. You might think you do, but you're actually counting on the concept again. Being able to work with real infinity would mean you're able to picture yourself all those nines up to the end. Since there is no end, you can't, i'm very sorry but we're limited. 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. 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. 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. 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. To finish i'd like to repeat my main points/theme (again? :p): A. Real infinity doesn't exist and it is impossible for us to grasp it. B. The mathematical concept of infinity hence isn't reality (or isn't infinity, but it can't be both, that would violate A ;)) C. The mathematical approach of infinity allows us not to remain stuck with the problem, but to remain able to work out calculations. D. If you refuse to make a distinction between mathematics and reality on this level, mathematics itself will pose you some paradoxes. Apologies for my bat habit of over repeating myself. Kind regards, Shark