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# 0.999 Repeating Equals 1

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Subutai
 Voting Style: Open Point System: 7 Point Started: 9/29/2013 Category: Miscellaneous Updated: 3 years ago Status: Post Voting Period Viewed: 1,276 times Debate No: 38275
Debate Rounds (3)

 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.Report this Argument 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.Report this Argument 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.abcdApplying 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/10000Applying 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)... = 0.9999P5: 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 = 1/10This 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.Report this Argument Con Haley123 forfeited this round. Pro Please extend my arguments and vote pro.Report this Argument Con Haley123 forfeited this round.
8 comments have been posted on this debate. Showing 1 through 8 records.
Posted by miketheman1200 3 years ago
Pro you devil you
Posted by miketheman1200 3 years ago
Pro you devil you
Posted by miketheman1200 3 years ago
Pro you devil you
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
Posted by Magic8000 3 years ago
I see you're debating Subutai on counter-intuitive math, I too like to live dangerously.
Posted by Haley123 3 years ago
i know...
Posted by Eitan_Zohar 3 years ago
Lol, there is literally zero argument for Con.
Posted by Subutai 3 years ago
Btw, the first round is for acceptance.
2 votes have been placed for this debate. Showing 1 through 2 records.