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# Does .999 repeating equal 1?

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after 4 votes the winner is...
LDPOFODebATeR0328
 Voting Style: Open Point System: 7 Point Started: 7/20/2014 Category: Education Updated: 7 years ago Status: Post Voting Period Viewed: 2,578 times Debate No: 59206
Debate Rounds (3)

 Pro The Con must prove how .999 does not equal to 1.First round is acceptance only.Good luck.Report this Argument Con P1.1+1=2P2.0.999+0.999= 1.998C1.1≠0.999Report this Argument Pro 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. 10x-x=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...Report this Argument Con I. ClarificationI 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. Cross-ExaminationMany 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 should3. 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. Report this Argument Pro 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 1-1/3 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.Report this Argument Con I've dug myself a really deep hole here.Give Pro the win. I'm not informed enough in mathmatical proofs to debate this.Report this Argument
18 comments have been posted on this debate. Showing 1 through 10 records.
Posted by thegoddamnreaper 5 years ago
Whoa, wait a second.
What makes you assume that 0.999... is a mathematical entity on which arithmetic operations can be performed?
Posted by LDPOFODebATeR0328 7 years ago
I was unable to put voting issues in my speech.
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.
Posted by AlexanderOc 7 years ago
If I was unsure of my proofs, they would not be put into a debate. Granted, my knowledge of mathmatical proofs is lacking and I may have missed an obvious flaw. If I did however I am sure my opponent will be eager to point it out.

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.
Posted by Samreay 7 years ago
Alex, just as a hint, you should try and check your math proofs in your latest argument in your conclusion, you might find one or two things that need addressing. Also, lucky the debate thesis isn't "Does modern math need an overhaul?", because that is a very, very large claim to make, especially for a high school student.
Posted by AlexanderOc 7 years ago
This debate is proof that modern math needs an overhaul.
Posted by KhalifV 7 years ago
Algebraic proofs are boring-,-. Bring on the analytic proofs!
Posted by AlexanderOc 7 years ago
My round 3 argument is incomplete. I misclicked submit prematurely.

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.
Posted by LDPOFODebATeR0328 7 years ago
Sorry for the typos, I don't know what happened. It was okay when I reviewd it.
Posted by Samreay 7 years ago
Should have known that unicode characters wouldn't be allowed. Sigh.
Posted by Samreay 7 years ago
This debate is sort of already over, but if you two like math debates, one that will surely require some solid explanatory skills is to discuss the Reinmann zeta function, where 1 + 2 + 3 + 4 + ... infinity = -1/12. Or, in better notation, _0;(W22;1)=W22;1/12.

You can read up on an explanation of it here (http://math.stackexchange.com...), if this sort of thing is of interest.
4 votes have been placed for this debate. Showing 1 through 4 records.