Does .999 repeating equal 1?
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The voting period for this debate has ended.
after 4 votes the winner is...
LDPOFODebATeR0328
Voting Style:  Open  Point System:  7 Point  
Started:  7/20/2014  Category:  Education  
Updated:  2 years ago  Status:  Post Voting Period  
Viewed:  1,578 times  Debate No:  59206 
Debate Rounds (3)
Comments (18)
Votes (4)
The Con must prove how .999 does not equal to 1. First round is acceptance only. Good luck. 

Thanks for accepting the debate.
I'd like to first start off with my definitions. According to the Free Dictionary, Repeating decimal is defined as a decimal in which a pattern of one or more digits is repeated indefinitely, for example 0.3535353535... Dictionary.com also defines repeating decimals as decimal numerals that, after a certain point, consist of a group of one or more digits repeated ad infinitum, as 2.33333 ". or 23.0218181818 ". This means .999 repeating is endless. In other words, there are infinite amount of 9s in .999 repeating. Here is a simple proof of why .999 repeating is equal to 1. 1/3= .333 repeating 2/3= .666 repeating 3/3= .999 repeating 3/3 also equals 1. Thus, 1=3/3. (1/3+2/3=3/3=1 is equivalent to .333...+.666...=.999...=1) 2nd Proof: 1. x=.999... 2. 10x=9.999... 3. 10xx=9.999....999... 4. 9x=9 5. x=1 6. 1=.99999999... (http://en.wikipedia.org......) Refutations: P1.1+1=2 P2.0.999+0.999= 1.998 C1.1X00;0.999 Judge, I'd like to point out that this argument is invalid. .999 REPEATING does NOT equal to .999. The topic clearly states: Does .999 REPEATING equal 1? Thus 0.999+0.999 is completely different from 0.999...+0.999... For all these reasons, please vote for the affirmative side of this debate. Thank you. Sources: 1.) Khan Academy https://www.khanacademy.org... 2.) Purple Math http://www.purplemath.com... 3.) Calculator http://www.calcul.com...... 4.) Dictionary.com http://dictionary.reference.com... 5.) The Free Dictionary http://www.thefreedictionary.com... I. Clarification I have a few things to bring up before starting my cross. First off, I must apologize my opponent for not saying "I accept" round 1. That was not at all implied by me accepting the debate. Second, if first round was acceptance, then why did my opponent bring up an argument for me to refute? He said, "Con must prove how .999 does not equal to 1." There is no reason why he should have said this other than to make an argument 0.999 and .999... are not equal to eachother and therefore making this argument is not even restating the resolution. I showed .999 is equal to 1 simply because I was told to, not to make an argument. Regardless, sorry for the rudeness. II. CrossExamination Many of Pro's arguments work only 1 way. As we all know, in math an equation must work backwards, forewards, sideways and upsidedown (metaphorically) to be considered a rule. There are a multitued of ways to refute the first argument. 1. If 1/3 is 0.3333.... and 2/3 is equal to 0.9999 then that means adding 1/3 is equal to increasing all digits beyond the decimal by 3. Ie. 0.6666... becomes 0.9999.... So, then increasing 0.6666...(2/3) by 1/3 will equal 0.9999... never 1. Same applies backwards taking 1/3 away from 3/3 (0.9999...) will equal 0.6666... (2/3) 2. If 3/3 = 1 then subtracting 1/3 (0.3333...) will not equal 2/3 (0.6666...) which it should 3. If 0.9999... was equal to 1 then 2 would be equal to 0.1818.... 3 would be 0.2727... 4 would be 0.3636... A number cannot equal a number with a lesser value. That destroys the meaning of them being equal. On to the next argument. The issue with this argument comes from subtracting a number for an infinite set of numbers. 

Thanks for the response.
Clarification: 1.) "Second, if first round was acceptance, then why did my opponent bring up an argument for me to refute?" I am sorry. It was quite ambiguous. I meant to say that it was Con's objective to prove how .999 does not equal to 1. :) Refutation: 1.) "So, then increasing 0.6666...(2/3) by 1/3 will equal 0.9999... never 1. Same applies backwards taking 1/3 away from 3/3 (0.9999...) will equal 0.6666... (2/3)" Like I said, 0.999... is equivalent to 1. .333... (1/3) plus .666... (2/3) equals .999... (3/3). 3/3 is equivalent to 1. Thus .999... must be equal to 1. I'd like to remind my opponent that .999...=1. He never proved how they were different. Instead, he merely stated."1/3 will equal 0.9999... never 1." Thus, my argument still stands. 2.) "If 3/3 = 1 then subtracting 1/3 (0.3333...) will not equal 2/3 (0.6666...) which it should" If you put 11/3 in the calculator, you get 2/3 (.666...). In order to prove me wrong, you must explain why the calculator is wrong. 3.) "If 0.9999... was equal to 1 then 2 would be equal to 0.1818.... 3 would be 0.2727... 4 would be 0.3636... A number cannot equal a number with a lesser value. That destroys the meaning of them being equal." First of all, your argument doesn't make any sense. 2 is clearly larger than .1818... I don't understand where you got these numbers from. Your pattern makes no sense at all. Second, we are only talking about the number 1. My second argument was dropped. Thus, it remains standing. I assume that he was unable to finish his previous speech. So, I urge him to continue. For all these reasons, please vote for the affirmative side of this debate. Thank you. I've dug myself a really deep hole here. Give Pro the win. I'm not informed enough in mathmatical proofs to debate this. 
4 votes have been placed for this debate. Showing 1 through 4 records.
Vote Placed by lannan13 2 years ago
LDPOFODebATeR0328  AlexanderOc  Tied  

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Total points awarded:  4  0 
Reasons for voting decision: Concession
Vote Placed by MrJosh 2 years ago
LDPOFODebATeR0328  AlexanderOc  Tied  

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Reasons for voting decision: My brain hurts from the poor math here. Arguments for concession.
Vote Placed by Samreay 2 years ago
LDPOFODebATeR0328  AlexanderOc  Tied  

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Reasons for voting decision: Easy win for pro, who presented an airtight mathematical proof in his opening argument that remained undefeated. Almost gave conduct to con though, because pro has an ambiguous thesis, where the debate title does not match his opening statement (the lack of the word "repeating" is of ultimate importance). Would have been good to see from both parties some of their math in latex via images.
Vote Placed by RyuuKyuzo 2 years ago
LDPOFODebATeR0328  AlexanderOc  Tied  

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Reasons for voting decision: Con conceded.
What makes you assume that 0.999... is a mathematical entity on which arithmetic operations can be performed?
Here it is:
1.) Source The judge ought to vote for the affirmative because the negative brings up no source. I brought up five. Thus, my argument were more reliable.
2.) Arguments My opponent brings up claims without evidence. I explained my proofs with detail, making my arguments more convincing.
Thank you.
Also, I did not mean that claim literally. I meant it as a joke, pointing a finger at the outliers of modern math that just need to be accepted as exceptions.
This is my own fault and I am not asking for consolation. I'm only stating this so nobody is confused at the adbrupt ending of my argument.
You can read up on an explanation of it here (http://math.stackexchange.com...), if this sort of thing is of interest.