0.999 Repeating Equals 1
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after 2 votes the winner is...
Subutai
Voting Style:  Open  Point System:  7 Point  
Started:  9/29/2013  Category:  Miscellaneous  
Updated:  3 years ago  Status:  Post Voting Period  
Viewed:  1,058 times  Debate No:  38275 
Debate Rounds (3)
Comments (8)
Votes (2)
This will be my second relaxing math debate. The resolution is that 0.999 repeating equals 1. No acceptance restrictions; 5000 characters; 48 hours to post arguments.
0.999 repeating forever. Infinte. Hmm... It's a little hard to think about. But you're always going to have one little tiny sliver of infinity left. One crumb left in the pie, you get it. "0.9999..." never ends. There will always be another "9" to tack onto the end of 0.9999.... So don't object to 0.9999... = 1 on the basis of "however far you go out, you still won't be equal to 1", because there is no "however far" to "go out" to; you can always go further. 

I would like to thank Haley123 for accepting this debate. P1. Any number can be expanded such that each digit place is represented: 0.a + 0.0b + 0.00c + 0.000d = 0.abcd Applying that to 0.9999... leaves: 0.9 + 0.09 + 0.009 + 0.0009... = 0.9999... P2. Convert the decimals into fractions: a/10 + b/100 + c/1000 + d/10000 Applying that to 0.9999... leaves: 9/10 + 9/100 + 9/1000 + 9/10000... = 0.9999... P3. Break up the fractions such that one x/10 exists and some y/(10^z) term exists: a/10 + b/10*(1/10) + c/10*(1/100) + d/10*(1/1000) Applying that to 0.9999... leaves: 9/10 + 9/10(1/10) + 9/10(1/100) + 9/10(1/1000)... = 0.9999... P4. Make those new fractions into tenths fractions with powersof10 exponents: a/10 + b/10*(1/10^1) + c/10*(1/10^2) + d/10*(1/10^3) Applying that to 0.9999... leaves: 9/10 + 9/10(1/10^1) + 9/10(1/10^2) + 9/10(1/10^3)... = 0.9999 P5: Use the Infinite Geometric Series formula: Because the statement in P4 is expressed as an infinite geometric series, that series's formula can be applied: 0.9999... = Where a = 9/10 and r = 1/10 This means that the formula now equals 0.9999... = (9/10)*(1/(1(1/10))) That equals: 0.9999... = (9/10)*(1/(9/10)) That equals: 0.9999... = (9/10)*(10/9) C. The right side equals 1, so the left side must equal one. Therefore, 0.9999... = 1 by the geometric series. Haley123 forfeited this round. 

Please extend my arguments and vote pro.
Haley123 forfeited this round. 
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8 comments have been posted on this debate. Showing 1 through 8 records.
Posted by miketheman1200 3 years ago
Pro you devil you
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Posted by miketheman1200 3 years ago
Pro you devil you
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Posted by miketheman1200 3 years ago
Pro you devil you
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Posted by shadowcelery 3 years ago
its easy to figure out.1/9 is .11 repeating 2/9 us .22 repeating until you get to 9/9 which is .99 repeating but 9/9 is also equal to 1. The easiest proof ever
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Posted by Magic8000 3 years ago
I see you're debating Subutai on counterintuitive math, I too like to live dangerously.
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Posted by Haley123 3 years ago
i know...
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Posted by Eitan_Zohar 3 years ago
Lol, there is literally zero argument for Con.
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Posted by Subutai 3 years ago
Btw, the first round is for acceptance.
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2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by Enji 3 years ago
Subutai  Haley123  Tied  

Agreed with before the debate:      0 points  
Agreed with after the debate:      0 points  
Who had better conduct:      1 point  
Had better spelling and grammar:      1 point  
Made more convincing arguments:      3 points  
Used the most reliable sources:      2 points  
Total points awarded:  4  0 
Reasons for voting decision: Pro's argument from geometric series is mathematically compelling and correct  Con's argument from crumbs is not. Arguments to pro. Con forfeits  conduct to Pro.
Vote Placed by drafterman 3 years ago
Subutai  Haley123  Tied  

Agreed with before the debate:      0 points  
Agreed with after the debate:      0 points  
Who had better conduct:      1 point  
Had better spelling and grammar:      1 point  
Made more convincing arguments:      3 points  
Used the most reliable sources:      2 points  
Total points awarded:  3  0 
Reasons for voting decision: I'm giving Con 1  0.999.... points.