.9999 repeating = 1

I'll try to be concise for everyone's sanity. :P "1. One this first point I don't even have to prove that infinity is a number or if it even is finite all I have to do at this point is to prove that infinity has value and can be applied in an equation." Whoa there buddy. First of all, I agree that infinity can be used in equations. Heck I posted a mathematical proof using infinity. But... I have no idea where you got the idea that you no longer have to prove that something doesn't have to have a last digit (or end) in order to put something after it. If I understand your argument, having one less digit at the END of the string of 9's is what would theoretically offset it. The structure of your argument is still dependent on proving infinite digits have an end instead of being more like a ray. I can understand why you would want to abandon your attempts to prove infinity is finite, but redefining what you have to do without justification is going a little far. If you are going to prove that infinity can be used in an equation, it has to be relevant to your point, such as using infinity in an equation the specific way you claim it can be used... just like I used infinity in an equation specific to evaluating .999 repeating here: http://i237.photobucket.com... "...mathematicians are not the final word on if infinity is a number not." So who is? If the global common knowledge is in agreement with the mathematical community concerning an issue, and someone declares a semantic perception of the issue, they are they ones to give infinity its "new and improved" definition? QUOTE: "I don't even need to prove that infinity is finite all I have to do is to prove infinity can have value and can be applied in an equation." Explain why. Using it in an equation is uneventfully common and well accepted in the mathematical community. Mismatching 9.9999......90 with .9999......99 is not. Putting digits on the end of infinity is like trying to hold the end of a circle. There is no end, hence the definition 'increasing without bound'. A bound would be the end; no bound means no end; no end means no last number. QUOTE: "% - 1 = %" First, this equation only demonstrates the point that infinity is not a number, because no number satisfies the equation. Second, different 'values' of infinity is a way of approximating the context of the equation. Rates of approaching infinity is simply a measure of say-- the coefficient. For example: 2% > % because it is a higher rate of increase without bound, this does not mean it is a higher infinity. For example, if you add up all the integers, you get infinity. If you add up all the even integers, you would get infinity but not at the same rate. Stating that infinity has values is rather inaccurate as .5 infinity does not really exist, especially when you realize that there is no precise value of 1 infinity. I recommend reading this: http://www.physicsforums.com... QUOTE: "I will answer a challenge that my opponent made earlier in the round when he ask me to show a number between 1 and .999…. To this I will answer with .9 to the infinity decimal place plus 1, now you may think this a ludicrous that there something larger then infinity but this has its support from my power of infinity sub point that shows how infinity can have different values and can be effected by math equations." This answer once again is dependent on a last digit in a repeating number. Your 'infinity can have different values' was imprecise, but more importantly didn't apply to your problem. simply put, manipulating the rate approaching infinity is VASTLY different than surpassing infinite digits. QUOTE: "if you divide 1 by 3 first you can't divide at all so you go to the digit behind the decimal then you 10 by 3 and you get a remainder 1 thus the answer isn't equal to one third, thus you do it again and divide 10 by 3 and get 1 remainder again and again" Thus it takes an UNLIMITED amount of 3/x, where x is a power of ten. I can see why you might think that because a remainder seems to always exist, an unlimited amount would also promote this. Its a common thought trap with a solution reminding me of Hilbert's paradox. The remainder is not unlike a taken room in a hotel. No matter how many rooms there are, if every one is taken, no more guests can be accommodated. Right? The answer is yes, until you consider the possibility of the oh-so-cool infinity. Since there is no limit, there is no reason why the people in the rooms can't be moved to their room number(n) +1, or maybe 2(n). This also demonstrates again, why infinity ISN'T really a number even though it can be used along side them. QUOTE: "Next my opponent uses another equation to prove his point but there are some key flaws." You have cited Wikipedia as a trustworthy source, so it might interest you to know that equation originally came right off of Wikipedia. I have some trouble understanding the apparent 'flaws' you see, but I will attempt to answer your questions. I cannot see any easy way to put an extra step in after evaluating the limit of a convergent sum, but your next question makes a little more sense. If you look up the properties of limits, it is perfectly legal to move certain numbers out of the limit notation. I wish I could help more but I don't know what it is that you don't know. :( For the first question I recommend learning how to quantify converging sums. Here is a good example using .111 repeating: http://en.wikipedia.org... Here is the article citing the proof I used for .999 repeating = 1, among others: http://en.wikipedia.org... This link is also provides a good math example for your first question: http://en.wikipedia.org... Beyond that, you go to say that you can make any number equal .999 repeating using this formula and quite frankly you lost me. :( QUOTE: "The law of functions- the problem with my opponent's attack on this is that both 1 and .9999… are in decimal form no if one was in fraction from while the other was in decimal I would agree that they could be in the same location but because the from they in it would prevent them from being in the same location." It was discussed in comments that you jumped to the conclusion that 1 is in decimal form, so I decided to point out a similar errors instead. The decimal system is proven to be able to communicate the same numbers with multiple notions. For instance, you claim that because both are decimal notion and written differently, they can't be the same number. This is incorrect, using a number other than .999 repeating to prove this, I submit the notation 1.00 repeating. Do you agree 1.00 repeating equals 1? QUOTE: "I would agree that they could be in the same location" Don't admit to that. ;J A few references: http://mathforum.org... http://mathworld.wolfram.com... uh.. that wasn't as concise as I planned. My apologies.