Is 0.999... repeating = 1.0 ?
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dmussi12
Voting Style:  Open  Point System:  7 Point  
Started:  2/8/2014  Category:  Education  
Updated:  6 years ago  Status:  Post Voting Period  
Viewed:  919 times  Debate No:  45478 
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http://www.khanacademy.org...
This video states that 0.99999... repeating is equal to 1. Please only respond with your arguments, not the ones from the video because I have already watched the video. I stand opposing the equality of the two numbers. The number .999... can be expressed as this sum: Sn=9/(10^n)=9/10+9/100+9/1000... This is a convergent series so, according to the convergence theorem, Sn=(9/10)/(1(1/10))=.9/.9=1 Therefore, .999...=1 http://en.wikipedia.org... This actually uses more 'correct' math than the video, which lies on several assumptions as it is intended for the general populace. However, I extend all arguments presented in the video to my argument as supplementary evidence. 

First of all, you know that the number 1 is rational. You also know that 0.9999... is irrational. If you were to say that 0.999... is equal to 1 than 1 is an irrational number (and vise versa.) Also, you cannot "prove" 0.999 repeating =1 using a mathematical formula. To do that you would need the fully complete number, and that is simply impossible. The fact is that 0.999 repeating will never reach 1, with every digit, it will get 90% closer, that gap just keep shrinking and shrinking and shrinking infinitely (which is why it is repeated infinitely.) If you could solve it mathematically, using simple subtraction, when you took 1 and you subtract 0.999... from it you would get 0.000...(1). Most people would say that with all those forever repeating zeros you would never reach the one. However,
You don't have to write an infinite amount of zeroes, you only have to put the repeat symbol above the 0 to represent the fact that the 0s are infinitely repeating. The 1 is there the whole time Rational number: a number that can be expressed as a fraction; the decimal form ends/repeats infinitely. 1 is rational, so is 0.999. It's 1's dec. expansion. Is .333 irrational? No, it equals 1/3. The relationship is the same. You can't prove 0.999 =1 using a mathematical formula. That's exactly what convergence theorem does, so you CAN apply the formula I gave. These theorems exist so we can rationalize complex problems and establish intrinsic problems of math It is the same thing with limits. These laws are accepted universally. You don't have to write an infinite amount of zeroes, the 1 is there the whole time You said that .999 would never reach 1, but now you're saying that 0.000 will eventually reach 0.001. The 1 is not just there, it doesn't exist. To put it in other words, picture the 1 at the end. Put a 0 in front of it. Repeat this infinitely, and you will never find the 1. Before you try to apply this argument to .999, try applying the convergence theorem formula to .000. 

F22Raptor forfeited this round.
As I have provided mathematical proof that remains unrefuted, and as my opponent has forfeited Round 3, I extend my arguments and implore at least one person to see this and vote PRO (I don't really want this to end in a tie when it certainly was not). 
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Posted by dmussi12 6 years ago
When I accepted this, I had no idea the character count was limited to 1,000. I had a nice 5,000 word rebuttal worked out, and I had to cut out a lot of information and summarize A LOT. I ask the voters to consider this before reaching a decision. I mean, I can put more into this comment than I could in the argument.
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Vote Placed by Mikal 6 years ago
F22Raptor  dmussi12  Tied  

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Reasons for voting decision: FF and just all round a beat down. Con was not able to refute anything pro brought up.