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The Instigator
Pro (for)
Losing
1 Points
The Contender
Con (against)
Winning
11 Points

# 0.999.... can't equal 1

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Post Voting Period
The voting period for this debate has ended.
after 3 votes the winner is...
kiddo
 Voting Style: Open Point System: 7 Point Started: 7/22/2013 Category: Science Updated: 5 years ago Status: Post Voting Period Viewed: 989 times Debate No: 35862
Debate Rounds (3)

 Pro Con must providde evidence as to why 0.999... Can equal Con may start immediatly so I can refute. Good luck.Report this Argument Con I shall use R1 for acceptance and leave side pro to provide arguments before presenting mine.I shall present inR2: Arguments and rebuttalsR3: Closing statement (rebuttals if pro acts in the same manner) Report this Argument Pro First of I would like to state that 0.999.... is practically a good option, and should continue in use as it would mess up a fewthings were we to change it. Second off the biggest problem with 0.999... repeating should not be 1 simply because even at infinite 9s there is still infinite more ways to make it smaller. People say we can't get that 0.000..;1 to fill in the number so we should assume it's not theren However we should assume it's there because that would defeat the purpose of 0.999.... repeating because it would mean it was both 1 and infinitely less than 1. This obviously doesn't hold much weight. I await my opponent tomake his arguments. I would also like to note that this is a learning experience personally, to see if I missed any evidence concerning this issue. So bring up anything concerning this issue. Thank you.Report this Argument Con Thank you once again Pro. to express this mathematically Pro arguments are inversely proportional to Con argumentstherefore, my arguments serves as rebuttals already in this case against Pro's arguments as well as a point. Argument 1: Fractionnow lets put the equation into fractions by dividing 3when 0.999... divides by 3, it equals to 0.333... also 1/3 when 1 divides by 3, it equals to 1/3 directly x=0.999.... y=1so here, x/3 = y/3therefore, X=YArgument 2: Algebralet x= 0.999... 10 x = 9.999...10x - x = 99x = 9 x = 1 Argument 3: Additional mathematics geometrical progression0.999... Separate into: 0.9 + 0.09 + 0.009....in this case a=0.9 r=0.1 Using sum to infinity formula a/1-r =0.9/ 1 - 0.1=0.9/0.9=1 I had fun revising my maths and add maths for tmr's paper, and still this is fun :D http://en.wikipedia.org...http://www.purplemath.com...;http://www.askamathematician.com...;Report this Argument Pro I thank my opponent very much. His aegument was thrilling to read. And I will concede that mathematically and algebraicly the notion holds true. Bit I still don't know how it is two values at the same time. Perhaps i am just understanding how math works, butbi was always taught that multiple representations may represent one value, but one representation does't represent two.. Thank you for your insights, and I ask you once again to prove me wrong.Report this Argument Con I once again thank my opponent for bringing up the debate, Truth be told, i think that is all the methods i have up my sleeves. Sorry >
5 comments have been posted on this debate. Showing 1 through 5 records.
Posted by Shadowguynick 5 years ago
Thank you, and I see why it is considered 1. Mathematics can be pretty illogical at times.
Posted by Shadowguynick 5 years ago
Arguement*
Posted by Shadowguynick 5 years ago
I would say con held the burden of proof. But i will put forth my own arfument anway.
Posted by DT 5 years ago
0.9 = 1 - (1/10)^1
0.99 = 1 - (1/10)^2
0.999 = 1 - (1/10)^3
0.9999 = 1 - (1/10)^4
0.99999 = 1 - (1/10)^5

The number 0.999999 with infinite progression of 9s can be expressed as a limit,

lim (1 - (1/10)^x) = 1, where x -> infinity

However, people forget that this answer is true only when applied with the limit theorem. All other approaches to the problem is essentially an expression of the limit theorem but re-stated in a different way.

But by definition the limit is merely the approximation of the convergence, and never really equal to the actual number it converges to.
Posted by kiddo 5 years ago
who holds the burden of proof?
I am interested
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