Does .999... Equal 1?
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after 1 vote the winner is...
SeventhProfessor
Voting Style:  Open  Point System:  7 Point  
Started:  10/30/2013  Category:  Miscellaneous  
Updated:  4 years ago  Status:  Post Voting Period  
Viewed:  911 times  Debate No:  39702 
Debate Rounds (5)
Comments (9)
Votes (1)
This will be a formal debate, following the following format:
Round 1; Acceptance Round 2; Opening arguments and rebuttal for contender. Rounds 35; Rebuttals, counterexamples, etc. Definitions = means absolutely equal to, not rounded in any way. .9r means .9 repeating. You must actually prove your point using either previously proven and/or universally accepted mathematical principals. This argument is in base 10. Please don't use any math that I know for a fact you don't understand, as there could quite easily be flaws neither of us see. The fact that .9r=1 is already universally accepted among the mathematical community shall be ignored for the debate.
I accept 

.9r certainly does equal 1. This can be shown with the following proofs, the first being an algebraic proof.
x=.9r *10 10x=9.9r x (which equals .9r) 9x=9 /9 x=1 x=.9r=1 Another proof can be made by taking an irrational number and subtracting it from its next highest integer, for example I'll use tau. 7.0000000000 6.2831853071...= 0.7168146928... As there is no last digit of tau, there can be no last digit of 7tau to, for lack of a better word, "bump it up" to exactly 7. Therefore, .7168146928...+6.2831853071...=6.9r. This means that: (7tau)+tau=6.9r Associative property of addition 7+(tau+tau)=6.9r Commutative property of addition (Unnecessary but makes it look nicer) 7+(tautau)=6.9r tau=tau, therefore tautau must equal zero 7=6.9r 6 1=.9r The last proof is the simplest. 1/9=.1r, multiply both sides by nine, and you get 1=.9r. You may argue that .1r is merely an estimation of 1/9, but it is exact, as the following proof shows; .1r=x *10 1.1r=10x x (which equals .1r) 1=9x /9 1/9=x 1/9=x=.1r I conclude my opening statement, and look forward to reading my opponent's.
I know this is supposed to be against it (and I am), but wouldn't this be the easiest proof: 1/9=.1 repeating 2/9=.2 repeating 3/9=.3 repeating 4/9=.4 repeating 5/9=.5 repeating 6/9=.6 repeating 7/9=.7 repeating 8/9=.8 repeating. So, by that logic 9/9=.9 repeating, but 9/9=1, so yeah. 

Noting a pattern and saying "following that logic" doesn't always work. I decided to prove that .1r is 1/9 and then multiplied both by nine, making it an actual proof. If I had done that, an easy argument could have been that you can't follow unproven patterns, as you didn't prove that any of those numbers are equal, even though they are. Let the voters note that all of my arguments still stand unopposed and the contender hasn't produced any arguments of his own.
tiger123198 forfeited this round. 

Con has forfeited this round, and still has not attempted to disprove any of my arguments. Vote Pro!
tiger123198 forfeited this round. 

Vote Pro!
tiger123198 forfeited this round. 
1 votes has been placed for this debate.
Vote Placed by Enji 4 years ago
SeventhProfessor  tiger123198  Tied  

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Total points awarded:  3  0 
Reasons for voting decision: Con's only argument was in support of the resolution, Pro wins.
no matter how many math calculation you throw at the con, you are destined to lose. you defined = as '= means absolutely equal to, not rounded in any way.'
0.9r may be equal to 1 mathematically, but it is certainly unequal to 1 literally e.g. the way you type it out, or the way you say it out (zero point nine nine nine........ versus one). so how come they are absolutely equal to each other?
without you specifying what equal means (limiting to mathematical sense or elsewise), we can only assume that 'absolutely equal' means 'definitely' and 'in all ways'.
thanks
0.999 needs a + 0.001 to become a whole I think.