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# Does .999... Equal 1?

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SeventhProfessor
 Voting Style: Open Point System: 7 Point Started: 10/30/2013 Category: Miscellaneous Updated: 5 years ago Status: Post Voting Period Viewed: 1,082 times Debate No: 39702
Debate Rounds (5)

 This will be a formal debate, following the following format: Round 1; Acceptance Round 2; Opening arguments and rebuttal for contender. Rounds 3-5; 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.Report this Argument .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 7-tau to, for lack of a better word, "bump it up" to exactly 7. Therefore, .7168146928...+6.2831853071...=6.9r. This means that: (7-tau)+tau=6.9r Associative property of addition 7+(-tau+tau)=6.9r Commutative property of addition (Unnecessary but makes it look nicer) 7+(tau-tau)=6.9r tau=tau, therefore tau-tau 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.Report this Argument 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.Report this Argument 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.Report this Argument tiger123198 forfeited this round. Con has forfeited this round, and still has not attempted to disprove any of my arguments. Vote Pro!Report this Argument tiger123198 forfeited this round. tiger123198 forfeited this round. 9 comments have been posted on this debate. Showing 1 through 9 records.
Posted by SeventhProfessor 5 years ago
If you add .0r1 to .9r, would you not get .9r1? There are ways for writing infinitely close to both 1 and 0, but .9r and .0r1 are not those.
Posted by ss11311086 5 years ago
and in my opinion, even from the perspective of math, 0.9r is not equal to 1. how much is 0.9r less than 1? 0.0r1. the difference between the two is infinitesimal, which is by definition not equal to 0. it's like a singularity in a function. if a function has a singularity at some point of it, may I ask is the function still continuous and connected at the singularity point or is it broken at that point? if your answer is that at the singularity point of the function, the function is not connected/continuous (broken by an unexplained point), then you should have no problem understanding why 0.9r is not equal to 1.
Posted by ss11311086 5 years ago
to pro:

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
Posted by KozWanderer 5 years ago
1 = Whole
0.999 needs a + 0.001 to become a whole I think.
Posted by crabby 5 years ago
SeventhProfessor, I didn't mean that the debate should not be brought up. I agree with you many like to argue the point. So in that sense it is debatable. Lol. The con side of it just never made any sense to me. No Tiger hasn't had much of a response. Maybe he was not expecting to have such a formidible apponent on the subject. Oh by the way sorry for the typos.
Posted by SeventhProfessor 5 years ago
I know, crabby. But when I mention this a lot of people I know say it isn't equal to 1. Tiger was supposed to give his best arguments and attempt to refute mine, but hasn't even tried. It's kind of sad, actually. I certainly do agree it's not debatable.
Posted by crabby 5 years ago
I do not see where this is even debatable. .9 is the same number as 1. It's just a different way of saying it. There are other examples of the same thing in numbers. If one argues that .9 is less than 1 then I would ask how much less than 1? Which no one seems to be able to answer. .9 repeating is a number. It must have a place on the scale of numbers? Repeating .9 doesn't get you any closer to 1. There are consequences of .9 not equaling 1. Which doesn't make a whole lot of sense to me. Either numbers make sense or they don't. I'm inclined to think they do. The consequences of .9 equally 1 make sense. The consequences of .9 not equally 1 does not.
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