0.999... = 1 | Prove Me Wrong

I usually make it a habit to not engage in arguments with people who don't seem open to reason or alternate opinions, which clearly is the case here. However, as I'm fairly new to Debate.org, I'll press on. I ask that you kindly be sure to respond to all of the claims made herein. Please bear in mind that as the Affirmative, the burden of proof lays with you. As such, it is incumbent upon you to prove, beyond a reasonable doubt, that each and every one of my contentions is faulty for one reason or another, ideally using logical arguments."Use common sense you can subtract an irrational number from an irrational number to get a rational number"Yes, you can. But you can also get an irrational number. The law I referenced has to do with the relationship between the simultaneous addition and subtraction of the same two irrational numbers (x and y). To rephrase: Take an irrational number x and another irrational number y...if (x - y) is rational, then (x + y) must be irrational; conversely, if (x - y) is rational, (x + y) must be irrational."No you're wrong actually I didn't say 10x - x = 9x = 9 I said 10x - x = 9x -x"Two glaring problems here. 1) You did say 10x - x = 9x = 9. That is literally the definition of your steps c and d, as copied below:c) 10x - x = 9.999... - 0.999...d) 9x = 92) Let's suppose you didn't, and that you actually said the mathematical statement you just posed in round 2:"I said 10x - x = 9x -x"Let's do some basic algebra:10x - x = 9x - xSimplify both sides9x = 8xDivide by common factor (x)9 = 8I'm quite certain 9 != 8 and I don't think you or anyone on this forum believes that it does. So, not sure where this was going."What idiot says 0.333... doesn't equal 1/3. "Despite the hilarious irony if you calling me an idiot, I also need to take exception to this point from the point of view of a person reading an English sentence. My contention was:"One cannot say that "1/3 = 0.333..." and then multiply each side by 2 to get "2/3 = 0.666"."In your attempt to discredit me as an "idiot", you conveniently left off the entire second half of my statement. This would be tantamount to saying that John Lennon once said, "You may say I'm a dreamer, but I'm not!""I didn't multiply I added. 0.333... + 0.333... = 0.666... It's very simple."I think you must realize that adding a number to itself is quite literally the definition of multiplication.Regarding your whole attempt to refute point 2, I think you (again) missed or ignored a key part of the argument. Please note the part that says, "placing ends to the unending decimals", which may also be known as rounding. It seems this entire instance of logical induction was lost on you. I never said that 0.3 + 0.3 equaled 0.7. My entire case here is that it does not. If it did, then perhaps your argument would hold water. However, the whole point is that 0.3 + 0.3 != 0.7. More precisely, the point is that ROUND(1/3,1) + ROUND(1/3,1) != ROUND(2/3,1). This holds for ROUND(1/3,2) + ROUND(1/3,2) != ROUND(1/3,2) and, most importantly, ROUND(1/3,N) + ROUND(1/3,N) != ROUND(2/3,N). Let me know if you'd like an Excel file proving this."I really think you're trying to misinterpret my proofs now. I'll make it toddlerly simple:0.999... < x < 1What is x?If you admit there is no answer then you admit 0.999... = 1."Despite the fact that "toddlerly" is not a word, I do appreciate you simplifying the argument so that someone of my lowly intelligence can understand it. I will attempt to respond with a marginally less condescending but, hopefully, more effective line of reasoning (or two).Marginally less condescending line of reasoning #1:Let's assume for just for a second that 0.999... is actually less than 1. If we can use deduction to start with that and show that there actually is a number between it and 1, your point will have been successfully (and irrefutably) defeated. Let's also use the variable h to represent an infinitely small number...the absolute smallest number you can think of. Perhaps this is (1e-((1e100 * 1e100)*(1e100 * 1e100))). Actually, no, let's say it's one one-quadrillionth of that. No, wait...one one-quadrillionth of THAT. We could keep going ad infinitum here, but you get the point.1) 0.999… < 1 [This is starting with the assumption that 0.999... != 1]2) 0.999… + h = 1 [h is that tiny, tiny, little, infinitely small number that makes up the gap]3) 0.999… = 1 – h [This says that we can take 1, subtract an infinitely small number from it, and get 0.999...]Marginally less condescending line of reasoning #2:This type of thinking borrows from discrete math and number theory, the same exact theory used to decide if sets are countably infinite or not (e.g. rational numbers vs. irrational numbers). Since searching for the smallest number possible is the same as searching for a number composed of an integer that follows an infinite number of zeros, it is perfectly suitable that we use the same type of thinking to show that there is a value between 0.999... and 1.I would ask that you give me a particular decimal string starting with 0.9 and continuing to the right with as many 9's as you'd like. Go ahead, I'll wait. For any number of 9's you give me, I will be able to give you a number that is between your number and 1. If you had all the time that existed in the history of the universe, you still would not be able to complete such a task. As the burden of proof lies with the Pro, I would ask how it can be that you allege this is true beyond a reasonable doubt if you cannot pass a simple test such as this."For the sake of the debate let's use the same calculator aka Google's calculator. You can find it by typing "calculator" in Google or Chrome..."First of all, you don't need to type "calculator" into Google or Chrome. You can just type the math equation and it will calculate. To the rest of this point, I am trying my best to explain that reaching a computational limit is not the same as reaching a mathematical fact. I think we can show this very clearly with a basic example:If you were to type, into Google, 0.88^9=, you would get 0.31647838182. However, using just an ever-so-slightly more powerful calculator, you would find that it actually equals 0.316478381828866. I think this should be a very simple proof of the fact that Google calculator should not be taken as the ultimate truth provider. In case you have doubts or think this is merely anecdotal, I would provide a few more examples: If you were to type, into Google, 0.39484823 * 0.948194914 = , you would get 0.37439308348. However, the actual answer is 0.374393083487902. If you were to type, into Google, (5.3E-2)^(12)*1E15 = , you would get 0.49125890425. However, the actual answer is 0.491258904256726. If you were to type, into Google, 3 * pi = , you would get 9.42477796077. However, the start of the actual answer (since it's irrational), is 9.42477796076938. Why are these examples particularly relevant? The first two examples reflect cases where not only are Google's answers truncated, they don't even round properly. If the answer to the first problem is going to be cut at the 11th decimal place, it should be 0.37439308349, not 0.37439308348. If the answer to the second problem is going to be cut at the 11th decimal place, it should be 0.49125890426, not 0.49125890425.The third example reflects Google's limited ability to deal with irrational numbers. I don't think anyone would deny that 3 * pi is a number that goes on infinitely. However, Google is not able to in any way indicate or reflect this. Rather, the answer is again truncated at the 11th decimal place. "I believe I have sufficiently taken each of Con's multiple arguments/"dis-proofs" and refuted each one using sound, established, proven mathematical and computational theory. I welcome any rebuttal or comments from the voting public."This comment is clearly on par with the general condescending nature of the rest of the argument. Though it would surely be inappropriate to speak this way in any case, it seems particularly imprudent to do so after using repeated arguments devoid of understanding of the underlying topic...especially when it's one chosen by the writer himself.