0.999... = 1 | Prove Me Wrong

I would like to kindly ask that Pro remove his/her condescending tone and aggressiveness from this debate. It has no place in logical discourse and is neither productive nor appropriate. But I digress...let's go step by step here. Note, I think Pro mislabeled their counterarguments here in terms of numbering, so I will try my best to match them up with mine."1. As I've said before it depends what x and y are that determine if you can subtract or add them"I am not talking about whether or not x can be subtracted from y, I am calling attention to an established theorem that regards the results of subtracting one irrational number from another. This has nothing to do with determining "if you can subtract or add them." This statement reflects a blatant misunderstanding of set theory. One can always add or subtract irrational numbers. The issue at hand is whether the result(s) are rational or irrational. You alleged that I should, "use common sense (to see that I) can subtract an irrational number from an irrational number to get a rational number." Yes, you can, but that doesn't mean you will. In fact, if you add two irrational numbers together and get an irrational sum, you can never get an irrational number when taking the difference between those two numbers."2. I'm sorry I didn't know you simplified the problem to 10x - x = 9x = 9. But yes if you plug in x you will see this equation is true."I'm not sure we can possibly have a reasonable discussion if Pro thinks that "if you plug in x (here) you will see this equation is true." Rather, if you plug in ANY x, you will see that this equation has no solution. Let's approach this algebraically then using specific examples.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.Using a few examples: Suppose x = 5 10x - x = 9x - x 10(5) - 5 = 9(5) - 5 50 - 5 = 45 - 5 45 = 40 Contradiction Suppose x = 0.001 10x - x = 9x - x 10(0.001) - 0.001 = 9(0.001) - 0.001 0.01 - 0.001 = 0.009 - 0.001 0.009 = 0.008 Contradiction Suppose x = pi (an irrational number) 10x - x = 9x - x 10(pi) - pi = 9(pi) - pi 9pi - 8pi 9 = 8 Contradiction No matter how you slice it, there is no value you can substitute for x (except for 0, which would be the trivial case) that makes this statement true. If Pro feels that this method of reasoning is proof that 0.999... = 1, I fear he/she is sorely mistaken and completely detached from elementary math."3. Sorry I mistyped that I meant 10x - x = 9.999... - 0.999..."I'm not certain which argument this pertains to."4. Once again you can't take away the ... it simply means the number goes on with 9's forever. 0.3 + 0.3 = ).6 how could it equal 0.7, please show me a proof. Give me the Excel please. By the way then lets not round.1/3 = 0.333...2/3 = 0.666...3/3 = 0.999..."Again, I think Pro lacks a fundamental understanding of basic mathematics and logic that makes this debate difficult to maintain. There is no proof in the world that shows 0.3 + 0.3 equals both 0.6 and 0.7. That is the entire point. I would urge pro to read up on Proof by Contradiction to get a better grasp on this common method of reasoning. Here are a few sources: https://en.wikipedia.org... http://www.math-cs.gordon.edu... As for the Excel, I don't know if I feel comfortable sending you something from my personal email address, but it should be abundantly simple for Pro to open up Excel and verify this in less than 10 seconds."5. This proof of yours makes no sense. Exactly you admit you couldn't give me a number as you gave me an "h". What is "h"? I don't think you understand the concept of infinity as there is no "tiny, tiny, little, infinitely small number" to make up the difference as ... means it goes on forever. Forever doesn't have a gap."For the third time, I must state that Pro lacks a fundamental understanding of the mathematics that underlie his entire claim. It seems they don't even understand what a variable is in the context of a proof. I don't need to provide a specific value for h, just like Pro, in their failed attempt to use algebra, didn't "need" to provide a value for x in their equation, "10x - x = 9x - 9". I would greatly beg to differ on my lack of understanding of infinity and would urge Pro to read up on a) the definition of a derivatives/differentiation and b) set theory before levying such allegations. Here are some resources:Derivatives https://en.wikipedia.org... https://math.stackexchange.com... http://tutorial.math.lamar.edu... Set Theory https://en.wikipedia.org... https://en.wikipedia.org... https://en.wikipedia.org... https://en.wikipedia.org... I think it is absolutely vital that Pro obtains even a basic understanding of these concepts before condescending toward me that my proof "makes no sense" and that I don't "understand the concept of infinity"."5a. Your number that you are waiting for is 0.9999... which is equal to 0.999... the ... means it goes on infinitely. The number of nines in ... is so much it's not even a number it's a concept."Again, please see my comments on derivatives, limits, and set theory as a complete lack of understanding thereof makes it difficult to have this conversation."6. Okay fine don't use Google use any calculator you want it says 0.999999999... equals 1. The calculator really doesn't matter."I'm glad Pro has finally conceded that one of their arguments was completely and utterly invalid. Since Pro asks me to "use any calculator (I) want", I will do so. Here are a list of just a few calculators/computers that will not show 0.999... equals 1 after at least one million9's: Hypercalc ja vascript Calculator Comptune Million Digit Base-N Calculator GNU BC Arbitrary Precision Numeric Processing Language Calculator Documentation: https://www.gnu.org... I'm hoping the voting public can see I've properly deflected Pro's generally-disrespectful attitude and also demonstrated his/her lack of a fundamental understanding of the very mathematical concepts they are invoking in addition to those that I am.Looking forward to the next round!