Does 0.9999 repeating 9 equal 1? 
Mrkai
Joined: Aug 07 2008 Posts: 361 Location: Virginia 
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Does 0.9999 repeating 9 equal 1?
as i see it 0.3 repeating 3 is onethird, right? and 0.6 repeating 6 is twothirds, right? what is 0.3 repeating 3 plus 0.6 repeating 6? 0.9 repeating 9. what is one third plus two thirds? 1. no rounding. no calculus limits involved. 0.9 repeating 9 equals 1? 
Brandon
Joined: Jun 04 2003 Posts: 4189 Location: St. Louis, MO 
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0.3333 is not exactly 1/3, but it's as close as we can get in decimal

HoolaKinG
Joined: Apr 24 2003 Posts: 938 
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It's like how if you looked at .8 repeating + .1 repeating most would assume that equaled .9 repeating...
But that is actually 8/9 plus 1/9 = 1 So no, .9 repeating != 1 
PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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Sorry, but you are rounding and that's where you introduce the error. 
corvettecrazy
Joined: Dec 17 2003 Posts: 4357 Location: moved (twice) 
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Is a stop sign a circle?
(The answer is yes with the correct definition of a circle.) For almost all applications the percent error by rounding .9repeating to 1 is negligible relative to the error caused by other factors. If you want to get technical, your statements
are inaccurate. Thus making your question inaccurate. 
PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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Not saying you're wrong but what definition would this be? It certainly doesn't fit the equation for a circle. 
clutch1
Joined: Oct 08 2006 Posts: 1928 Location: around hurr. 
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The plane will take off.

justinwebb
Joined: Sep 15 2004 Posts: 3170 Location: Columbus, OH 
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oh god not this debate again 
Mrkai
Joined: Aug 07 2008 Posts: 361 Location: Virginia 
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I say they are equal. There's a funner geometric series proof, but I don't have time to post it now, so I'll update later. Here's one though I really like.
x = .9 repeating 10x = 9.9 repeating 10x x = 9.9 repeating  .9 repeating 9x = 9 x = 1 so 1 = .9 repeating so try to find my fault in that^^^ theres isnt one. 
kornholio788
Joined: May 02 2005 Posts: 9748 Location: Tosa, WI 
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.3 repeating is not 1/3. We just say it is one third as it is extremely close and easier to say.
.9 repeating is extremely close to 1. I don't understand how you can not understand something so simple. 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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ummmm, 1 doesn't equal anything but 1 there is a fault. you place the given in for x and it already solved you can't go on from there. x = .9 repeating 10x = 9.9 repeating 10*.9 repeating=9.9 repeating 9.9 repeating = 9.9 repeating MATH OWNED 
Mrkai
Joined: Aug 07 2008 Posts: 361 Location: Virginia 
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if two numbers are not equal, there is a third number that is also unequal and that can fit in between them on the number line. Regardless of the type of real number or the difficulty in computing its value or representing its value ,there does exist a number that is larger than one but smaller than the other.
x<y<z 0.9999<y<1 If 0.9999... does not equal 1, then what number, y, could exist in between them such that math? Since there is no conceivable number that can exist in between the two, they must be equal according to the definition of the real numbers as a continuum. http://math.wikia.com/wiki/Proof:The_Decimal_0.999..._is_Equivalent_to_1 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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too bad 9.9 repeating doesn't equal 1 so its wrong.

harris_23
Joined: Nov 03 2008 Posts: 134 Location: Warwick, Rhode Island 
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funner!? really? i don think im gonna take any advice that comes from the person that says funner.. lol and not to mention you could plug any number into that variable and it is true! 10 times any x then subtracting x will always give you 1.
this is true but there is a number between .9 repeating and 1. it just is not a real number but it does exist its just a figure of rounding. 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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but he did the problem wrong, he didn't use order of operations. 
harris_23
Joined: Nov 03 2008 Posts: 134 Location: Warwick, Rhode Island 
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^^^ obviously lol but i was just goin off of what he had posted.

PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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You're wrong in the second step. Your error comes in the basic understanding of rational and irrational numbers and how you can use arithmetic operations. Without and approximation or rounding ever so slightly, you can NOT use an arithmetic operation (+, , /, x, ^, etc.) on an irrational number. When you do use an arithmetic operation on an irrational number, you approximate the answer. Just as you can not multiply Pi by 10 w/out a little error, you can not do: 10*0.9 repeating You are taking an irrational number, temporarily making it rational so you can multiply it by ten, and then rounding and making it irrational again. The same holds true w/ the original post. You can not perform the operation 0.3 repeating plus 0.6 repeating w/out an approximation. 1/3 is a RATIONAL number and you can perform arithmetic operations w/ it. 0.3 repeating is an IRRATIONAL number and you can NOT perform arithmetic operations w/out approximations. *EDIT* The "number" that would fall between 0.9 repeating and 1 would be: 0.9repeating + [0.1*10^(infinity)]/2 But you can not compute that number because you can not use arithmetic operations on irrational numbers (ie, 0.9 repeating and infinity). You can calculate the limit of the equation but that's just an approximation and not an exact number. 
PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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Let x = 3 10x = 10*3 10xx = 10*33 9x = 27 x = 3 I fail to see how that give me 1. 
jdusty914
Joined: May 09 2004 Posts: 1623 Location: Tennessee 
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Mrkai, if you have sat through any math or science type of class you would know that no matter what 0.9999999999999999999999999999999999 repeating is not equal to 1....If you were to take the limit as the variable or whatever tends towards infinity then it would come very close and most people might just say that it is 1 but they all are wrong....there is no way possible for 0.9999 repeating to be equal to 1.....At some point you have to round your number to get it equal to 1.....if you set up an equation like the ones on wiki about does 0.999 equal 1 then they say yes and give proofs, but i still say that it does not equal 1.....

PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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Limit of the infinite series DOES equal 1. The limit is not the answer, the limit is the number that the infinite series approaches and will come infinitely close to (but never technically reach). ie. the lim(1/n) as n > infinity = 0 In reality, no matter how large "s" becomes 1/n will never equal zero. It will approach zero, but it can never become zero w/out an approximation. But, the lim(1/n) as n > infinity does equal zero. The same thing is true if you take the sum/limit of the infinite series for 0.9 repeating. The sum of the infinite series will come to 0.9 repeating but the limit of the series as "n" approaches infinity does equal 1. 
TRogers
Joined: Feb 09 2005 Posts: 6083 Location: Ohio 
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Skimming through this thread made me feel like this,

HTown
Joined: Dec 10 2008 Posts: 1186 Location: Houston, TX 
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that picture fits perfect.

Mrkai
Joined: Aug 07 2008 Posts: 361 Location: Virginia 
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but 0.9999 repeating IS a limit.
0.9999 ... = %u03A3 (n=1 to k) 9/10^n (where k is the number of 9's) 0.9999 repeating is the limit of that series as k approaches infinity. lim (k>%u221E) %u03A3 (n=1 to k) 9/10^n = 1 Therefore, 0.9999 repeating equals 1. 
PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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A limit is NEVER going to be an irrational number. A limit will always be a rational number (hence the purpose of a limit). I do know the equation you posted. It's the infinite series for 0.9 repeating. The ANSWER to that equation is 0.9 repeating. The LIMIT of that equation is 1. They are two seperate things. The answer is the exact number of the sumation when it's carried out to infinity. The limit of the equation is the number that the sumation approaches. If you continue to add them together as n approaches infinity, it will get ever closer to 1 but will never actually reach the number 1. You can see my earlier post where I showed you an equation for the number that would fall between 0.9 repeating and 1. But you can not calculate it as 0.9 repeating is an irrational number. Obviously you don't know what you're talking about. You seem to be Google searching and posting what other people say (or else your "equations" would be more than a series of symbols created from copying and pasting). I'm not going to argue w/ you about it b/c one can not prove a point to someone who doesn't have the basic subject knowledge to fully understand the subject at hand. You MUST understand that you can NOT perform arithmetic operations to an irrational number w/out approximating. 
Golfer
Joined: Aug 23 2004 Posts: 1290 Location: Milwaukee, WI 
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Mrkai is right.
This has long been accepted by the mathematical community. .9 repeating denotes the same real number as 1 
Cooper
Joined: Mar 19 2006 Posts: 1770 
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This reminds me of the brain teaser where your hand is a foot away from the door knob and so you reach for the knob by halving the distance between your hand and the knob, then halving it again, then again, and so on ad infinitum, never actually touching the knob .
But then someone suggests this is ample reason to assume door knobs can never be touched . The halving of the distances between the hand and the knob is like the continuation of the .9 number, its purely theoretical . Its doesn't practically manifest itself in the 'real' world . In the real world we just open the darn door . Just as in the real world .9999.. is 1 . But since your asking the question as a theoretical exercise, I side with PwrRngr in that the realworld implications don't matter . Its never strictly identical to 1 in terms of pure mathematical theory . As he said, at some point during each of the proofs offered the number leaves the realm of pure mathematics and becomes 'real', which is what (falsely) gives the result of 1 . 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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MrKai, and Golfer are idiot.
nothing equals one except 1 1=1 thats it 324589i05243 doesn't equal 1 because i say so. 
Brandon
Joined: Jun 04 2003 Posts: 4189 Location: St. Louis, MO 
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1/3 = 0.33333
0.33333 * 3 = 0.99999 1/3 * 3 = 1 Therefore 0.99999 = 1 Problem solved. 
PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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Again, applying arithmetic operations to an irrational number results in an approximation. You can not multiply 0.3 repeating w/out introducing error. 1/3 is a RATIONAL number. 0.3 repeating is an IRRATIONAL number that's an approximation of the rational number, 1/3. They are not exactly equal in a theoretical sense. 
Brandon
Joined: Jun 04 2003 Posts: 4189 Location: St. Louis, MO 
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I'm just using logic. If we assert that A = B and B = C, then A = C. If you say that 1/3 does not equal 0.3333 because its irrational, then this thread is worthless because 0.99999 is irrelevant.

ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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you dont use logic in math, you use math in math. [/b] 
PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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In the theoretical sense of the "proof" at hand, 1/3 does not equal 0.3 repeating. This is where the error comes into the problem and why the proof doesn't work. 
SickWitIt
Joined: Aug 03 2006 Posts: 5840 Location: Piqua, Ohio 
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Apparently I was wrong, we DO have smart ppl on Oznium..
Me not included. 
clutch1
Joined: Oct 08 2006 Posts: 1928 Location: around hurr. 
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Hahaha 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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vagina. 
Mrkai
Joined: Aug 07 2008 Posts: 361 Location: Virginia 
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Suppose .9999999999 (repeating) is not equal to 1.
Then these are two distinct numbers, call them x and z. Then there exists a y such that x + y = z. i.e. (by the additive inverse property). So since x = .99999999 repeating, y = .00000000000 repeating and finally a 1. How many 0's are there? If there are finitely many 0's (say n) then y = 10^n. This contradicts that x has infinitely many nonzero digits since x + 10^n = z So y must have an infinite number of 0's before the 1. But if y has an infinite number of 0's then y = 0. Then it follows that x = y, i.e. .999999999 (repeating) equals 1. 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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the is no such thing as repeating zero. Idiot. Do you seriously beleive this ****?

PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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You're still thinking finite. You simply don't have a good enough understanding to comprehend the problem. I gave you the equation for the number in between .9 repeating and 1. Ignore it or try to figure it out, it's up to you. This should throw your brain in a loop. Suppose I add up all the prime numbers from 1 to infinity. The total of all these prime numbers will be infinity. Now, suppose I add up ALL the numbers from 1 to infinity. The total of all these numbers is also infinity. But, the infinity from adding up all the numbers is greater than the infinity from adding up all the prime numbers. How can this be? Does infinity not equal infinity? 
Mrkai
Joined: Aug 07 2008 Posts: 361 Location: Virginia 
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thats is my point 
Mrkai
Joined: Aug 07 2008 Posts: 361 Location: Virginia 
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true. 
kornholio788
Joined: May 02 2005 Posts: 9748 Location: Tosa, WI 
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ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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perfect pic! this thread is all kinds of dumb. 
Golfer
Joined: Aug 23 2004 Posts: 1290 Location: Milwaukee, WI 
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Don't ever call me an idiot you piece of ****. I have a Bachelors in Mathematics from UWMadison, one of the top undergrad and graduate math programs in the world. As I said, .9 repeating denotes the same real number as one. If you do not know what this statement means, don't bother posting. I have seen various proofs of this problem, all of which were presented by people with PHD's in Mathematics. The problem is right, anyone arguing against it is wrong. 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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You have a Bachelors in Mathematics and you think .9 repeating=1? Wow just wow. Chill out BRO, it's just the interwebs. 
PwrRngr
Joined: Jul 19 2007 Posts: 4407 
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He did not say 0.9 repeating equals 1. He said that 0.9 repeating denotes the same REAL NUMBER as one. This is not the same as saying 0.9 repeating equals 1. 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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What's the difference, i thought that meant the same thing as equals? I could really give a **** though, .9 repeating=.9 repeating and 1=1 i don't see how any other number can equal another number. 
pOrk
Joined: Jan 03 2004 Posts: 8391 Location: Milwaukee Wi 
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My brother is the last person you want to argue mathematics with, I can guarantee you that. Madison is a top 10 School, and it is at THE top for Mathematics, which is what is degree is in 
Golfer
Joined: Aug 23 2004 Posts: 1290 Location: Milwaukee, WI 
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You don't see how other numbers can equal another number because you sir are the idiot. Once you take some math courses, come back and argue. I don't mean calculus, discrete, differential equations, etc. I mean some real math courses. Abstract / Modern Algebra, Theory Of single/multivariate calculus, Topology, hell even a strong Combinatorics class, then come back and argue. Until you understand the most basic of math proofs, please do not try to argue about them. 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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SO 1=2?
that makes math SOOOOO much easier. 
Golfer
Joined: Aug 23 2004 Posts: 1290 Location: Milwaukee, WI 
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Ah, yes. But then I will argue that if two numbers have the same real value, are they not equal? 
Golfer
Joined: Aug 23 2004 Posts: 1290 Location: Milwaukee, WI 
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If math was easy then Mathematician would not be the TOP RATED job in America, nor would Actuary be number 2 , nor would they be the highest paid. Math gets extremely complex. As I am sure PwrRngr can tell you. I am guessing he has taken quite a few math courses. Engineering Student perhaps? 
ViciousBread
Joined: Aug 31 2008 Posts: 887 Location: GString Town Arizona 
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i didn't say math was easy. 
GoldenRod
Joined: Oct 27 2003 Posts: 709 Location: Long Island, NY 
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GoldenRod
Joined: Oct 27 2003 Posts: 709 Location: Long Island, NY 
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A source of the job ranking statement: They're also fairly high in the top salary rankings: http://www.myplan.com/careers/top_ten/high_pay....8c34acb004c9754fd13af0ba5107eb7a 