0.999... is equal to 1
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JustVotingTiedDebates
Voting Style:  Open  Point System:  7 Point  
Started:  7/7/2016  Category:  Education  
Updated:  10 months ago  Status:  Post Voting Period  
Viewed:  632 times  Debate No:  93439 
Debate Rounds (3)
Comments (16)
Votes (2)
I accept. 

0.999... can never equal to 1 as there is an infinitesimally small difference between that and 1.
This, Pro might argue, is exactly the reason why it is equal to 1, as the infinitesimally small difference is negligible. As the 9's progress, the difference is getting closer and closer to 0. Since there is an infinite number of 9's, the difference might as well be 0. This argument is ridiculous. Infinitesimals are used all the time in calculus. In fact, infinitesimals is root of calculus. So, statements such lim(x>1) (x/(x1)) would make no sense. Infinitesimals require there to be a difference. Infinitesimals is a well defined concept and used frequently.
Simple. 0.33 = 1/3 0.66 = 2/3 0.99 = 3/3 = 1 I strongly ask voters to vote by power of debate not by their own opinions. Thanks, Adil, Qatar. 

1/3=0.333.... and 2/3=0.6666....... Fine, I get these two.
But, how do you say, 0.33333....+0.666....=0.9999....? Addition is not defined for these numbers. You would have to define all the arithmetic operations to even say that 0.333...+ 0.666...=0.999.... To put it simply, you have not proved all the operations working on normal, rational numbers would work on this mathematical entity, this repeating decimal number. Argument in the comments: The "algebraic proof" goes like this. Let x=0.9999.... 10x=9.9999... 10xx=9.999...0.99999... 9x=9 x=1 The same problem lies with this argument. There is no proof of why the arithmetic operations would work on repeating decimal numbers. Making an axiom out of this fails too. For that matter, you could have made an axiom straight away stating 0.9999...=1 The opponent is required to make an argument for the same without creating unnecessary axioms. And, as Pro said, vote based on the power of the debate, not on your preconceived notions.
I have two things to say in the last round. 1. I heartily thank my opponent for giving me another proof that 0.999=1 which is: Let x=0.9999.... 10x=9.9999... 10xx=9.999...0.99999... 9x=9 x=1. 2. You say: "But, how do you say, 0.33333....+0.666....=0.9999....? Addition is not defined for these numbers." I never said that. Please read my argument in the second round again. So everybody, I repeat: There are two proofs that 0.999=1 1. 0.33 = 1/3 0.66 = 2/3 0.99 = 3/3 = 1 2. Let x=0.9999.... 10x=9.9999... 10xx=9.999...0.99999... 9x=9 x=1 VOTE PRO. I strongly ask voters to vote by power of debate not by their own opinions. Thanks, Adil, Qatar. 
2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by lord_megatron 10 months ago
thegoddamnreaper  JustVotingTiedDebates  Tied  

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Reasons for voting decision: Con accidently gave another proof to pro. Pro use mathematical analogies that con couldn't rebut. Con said there is is an infinitesimally small difference between 0.99 and 1, but pro's mathematical analogies show that it is equal. The first one was since 1/3=0.33, 2/3=0.66, 3/3=1 or 0.99 therefore they are equal, and x=0.99 10x=9.99 10xx= 9 9x/9=1 x=1.
Vote Placed by Sashil 10 months ago
thegoddamnreaper  JustVotingTiedDebates  Tied  

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Reasons for voting decision: CON argued that there will always be an infinitesimally small difference between 1 and 0.9999 while PRO offered a mathematical proof showing that 1 is infact 0.9999... CON claimed that Addition is not defined for these numbers but since it's undefined there's no way to prove the credibility of PRO's proof. Since the proof couldn't be proven right we face a stalemate kind of situation in this debate. But I'm going to give the benifit of doubt to PRO here because CON never explained why such operations on the said numbers should be considered undefined. There aren't any sources supporting his statement nor is there any rationale provided as to why one must consider so.
And btw PRO when you said "I never said that(about addition). Please read my argument in the second round again."
You multiplied 1/3 by two which is necessarily adding 0.3333 + 0.3333. If CON had more cogently pursued with his argument of the operation being undefined you could have very well lost this debate.
Try solving this problem then :
Three friends A, B and C  go boating in a stream and decide to play a game. B and C are at a point X at time t = 0 seconds. B is on a boat which is floating with the stream and C is on a boat which is anchored at X. Both B and C release paper boats at intervals of 5 seconds, beginning at t = 0 seconds, A starts from a point Y, downstream of X, at t = 0 seconds and starts collecting all the paper boats he encounters as he rows upstream towards X. The speed of A"s boat in still water is thrice the speed of the stream. Find the total number of paper boats collected by A, if B reaches Y at t = 132 seconds.
P.S: This doesn't involve any complex mathematics :P
1=5 so 5=1
In vote.
1=5
2=25
3=125
4=1125
What is 5=??
;)