.9999 repeating = 1

A side note: Please proofread your debate, as it is growing increasingly harder to understand you. :P Alright lets get jiggy with it: DEBUNKING THE OPPOSING ARGUMENT: Q-"My opponent tries to argue that infinity increases at a different rate" Perhaps I was unclear or simplifying. There is one infinity (the concept of boundlessness) and equations can make variables or other equations approach infinity at various rates. Q-"It shows how infinity can have multiple values and can be applied in math." I already told you that using infinity in math wasn't the problem... We both agree it can be used in math. FOR EXAMPLE: Limit as x approaches %, for the function: f(x) = x is %. This translates to, as x gets bigger it approaches no end and no boundary to become arbitrarily close to. It approaches infinity without reaching it, because infinity is boundless. X increases without bound, as does y or to hold the notation used earlier: f(x). Because its used in equations, you illogically presume it has a definite value, with a definite number of decimal places. Q-"this only proves my point if % were = 1 the %+1=2" I'm assuming you meant "if .999 repeating = 1 then .999 repeating + 1 =2" Which I would agree with. Infinity does not equal 1. Otherwise, those people in stores who give out food samples with signs saying please take one, would get royally screwed. ;) Q-"the they way that they are used in an equation the second on would be bigger this can be applied to the rhs lhs equation" Uhh I'm still waiting on the example or source for using an infinite number of decimal places as opposed to in infinity. Besides, an increasing rate of approaching infinity, would not be quantifiable. There isn't even a variable for time. Have you taken any class covering limits? :X Q-"this way I said all I have to prove is that % has a value and can be applied in equations." Value is different than rate. Rate is different than notion expressing unbounded. Repeating decimal notation is not the same as coefficient rate determination. Read above please. Q-"The first point that my opponent makes is that it is illogical to have a 0 at the end of the repeating 9's but there is nothing illogical about this" There is no end to put the decimal after. Limitless, endless, boundless, I don't know how else to say it. :( Q-"so the same can be applied to the 0 at the end while the 9's in between continue to grow and end in 0" A number line has numbers grow, but your example assumes they are not the same number as its own proof. [label a] Circular logic works, because [go to label a]; .9's adding is founded on the idea that we have numbers in between .999 repeating and 1. Your proof is invalid. Sorry. Q-"it is not he rate that it is approaching infinity it the speed at which is growing" My daily fill of lol's. I'm not so sure there is a distinct difference, but rate is the word mathematicians use. Speed tends to reiterate the distance / time relationship. See above (again). How is this a 'contradiction' or a by-product of you having to prove the finite properties (end/edge) of infinity? Q-"if infinity constantly increasing they it would be imposable to use in an equations" Your definition of infinity needs revision, but I think its my fault for being vague earlier. I will simplify: There is a positive and negative infinity that exists conceptually. Values of (or in) equations can try to reach these values at different rates. Q-"Next my opponent tries to disprove the argument about the remainder with is example but this example is inadequate to describe to represent it" When applied to the number of decimal places, and NOT the 'value' of infinity, it works fine. It merely demonstrates that there is no bound to the repeating 9. Q-"Also don't even listen to my opponent's argument" Classy. If you were truly correct in your disproof, you wouldn't need to direct people away from it. Q-"first I would like to point out that my opponent conceded the argument that 1/% is only approximately 0" I did no such thing! Libel I say! I specifically did a ctrl-f to find every "0" and went through and read every instance just in case I mistyped something. Not once did I say 1/% is approximately 0. I'm glad that the history is still open for viewing so that the voters can check this for themselves! (Be sure to make sure that within a post it is not a quote of another.) I'm kinda pissed now. >:( Q-"don't let him bring this up in his next speech because this is his final speech and being new arguments in is abusive because there is no time to debate them" You brought up a point, and said don't let me debate it because there isn't time to debate it? 1. You brought it up 2. You have another posting opportunity giving me the disadvantage EVEN if I do post. 3. It was either a VERY careless mistake or a blatant lie. Why can't I mention it? Too late I did. Q-"my opponent argues that there can be multiple examples of 1 in a decimal form that can be at the point of 1 but the example of 1.00 doesn't prove me wrong because we simply by removing the 0's behind the decimal making be 1" You manipulated it. Have HONOR! Subtracting zero's doesn't do anything to the value but it does change the way it is written ...which is the point. Q-"The next thing he says is that I conceded that they could be in the same location if only for that 3 letter word called "but" that is right after that statement saying how them being in the same locations is imposable." I will answer this with another quote. See below this time. Q-"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." Assuming 'from' was supposed to be 'form', I already demonstrated that 1.00 is another decimal form for 1. Returning to this quote: Q-"My opponent's opponent again tries to make have to prove that I have to prove that there is a final digit in the repeating 9's" I would also like to post this quote. It was regarding your rhs and lhs experiment and number philosophy constructing the foundation for your entire argument: Q-"But the problem with this that if infinity did equal a finite number then the nines would have to stop a t some point." "the next problem with the equation that I had was how he went from 9/10 k to 1-1/10n there is no way that that 9 becomes a 1 thus creating a huge flaw in the equation" I believe I understand you point more now, but since this is my last post I am not allowed to defend it. Are having trouble seeing how 9/10 = 1 - 1/10 Or 9/10 + 9/100 = 99/100 = 1 - 1/100 Get it yet? : SUMMARY (to the voters): My opponent has failed to present an argument that did not rely on adding another decimal on the end of and endless string of numbers. He failed to present mathematical evidence or citations for the form .999.....90. He failed to debunk any of my proofs (listed again below). He has abandoned the premise that he needs to prove that infinity has an end in order to attach something to it. He failed to respond to several minor challenges including 'who is an authority if mathematicians aren't'. MAIN PROOFS: PROOF 1: 1/3 = .3333 repeating. Therefore: 1 = 9/9 = 3/3 = 1/3 + 1/3 + 1/3 = (.333 repeating) times 3 = .999 repeating PROOF 2: Let x = .999... 10x = 9.999... (multiplying RHS and LHS by 10) 10x - x = 9.999... - x (subtracting x from both sides) 9x = 9 x = 1 .999... = 1 (My opponents only attack against this was revealed in the last quotes I posted under the debunking section. It returns to the dependency on a 'finite' infinity.) PROOF 3: A simple Calculus solution that I hope I have cleared up for my opponent: http://i237.photobucket.com... VOTE PRO! XD No letters lef