The Instigator
Subutai
Pro (for)
Winning
7 Points
The Contender
Haley123
Con (against)
Losing
0 Points

0.999 Repeating Equals 1

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Post Voting Period
The voting period for this debate has ended.
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: 1,137 times Debate No: 38275
Debate Rounds (3)
Comments (8)
Votes (2)

 

Subutai

Pro

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.
Haley123

Con

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.
Debate Round No. 1
Subutai

Pro

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 powers-of-10 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

Con

Haley123 forfeited this round.
Debate Round No. 2
Subutai

Pro

Please extend my arguments and vote pro.
Haley123

Con

Haley123 forfeited this round.
Debate Round No. 3
8 comments have been posted on this debate. Showing 1 through 8 records.
Posted by miketheman1200 3 years ago
miketheman1200
Pro you devil you
Posted by miketheman1200 3 years ago
miketheman1200
Pro you devil you
Posted by miketheman1200 3 years ago
miketheman1200
Pro you devil you
Posted by shadowcelery 3 years ago
shadowcelery
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
Posted by Magic8000 3 years ago
Magic8000
I see you're debating Subutai on counter-intuitive math, I too like to live dangerously.
Posted by Haley123 3 years ago
Haley123
i know...
Posted by Eitan_Zohar 3 years ago
Eitan_Zohar
Lol, there is literally zero argument for Con.
Posted by Subutai 3 years ago
Subutai
Btw, the first round is for acceptance.
2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by Enji 3 years ago
Enji
SubutaiHaley123Tied
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Total points awarded:40 
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
drafterman
SubutaiHaley123Tied
Agreed with before the debate:Vote Checkmark--0 points
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Total points awarded:30 
Reasons for voting decision: I'm giving Con 1 - 0.999.... points.