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0.999r=1? Discuss

Intergalacti...	Date: August 4, 2005 @ 7:58 PM Any mathmeticians out here? Please discuss on whether you think 0.9r = 1 or not
sinai	Date: August 4, 2005 @ 8:01 PM or better yet...gimme the exact answer to 22 divided by 7
evansorchid	Date: August 4, 2005 @ 8:16 PM I don't mean to be rude...but it's spelled mathematician.
shadowself	Date: August 4, 2005 @ 8:39 PM Depends on if you go by the title or the first post. r=1.111111 if 0.9r = 1. r=1.001001 if 0.999r = 1.
Apertome	Date: August 4, 2005 @ 9:48 PM 0.9999 ... = 1, yes. Think: 1/3 * 3 = 1 0.33333 ... * 3 = 0.99999 ... 1/3 = 0.33333 ... So: 1/3 * 3 = 0.33333 ... * 3 = 0.99999 ... = 1
kingo	Date: August 4, 2005 @ 9:50 PM show-off. : pi : :neck:
RobertMcDade	Date: August 5, 2005 @ 2:10 AM sh+44 5t+sgf 65+63 46-p6e=13c-4334 46f57s g/sdg55 64*455 dfg=e rt67
DaveWL	Date: August 5, 2005 @ 5:22 AM By 0.9r I think you mean 0.9 recurring - so a number with an infinite numbers of 9s after the decimal place. Scientifically I think that equates to a number less than 1. In practice there is always going to be a rounding up of the number whether it’s the 2nd, 3rd, 100th or 1000th decimal place. Are you paying attention at the back there?
ChillinBuzz	Date: August 5, 2005 @ 6:55 AM picky buggers
kingo	Date: August 5, 2005 @ 7:34 AM DaveWL -- actually it equates to exactly 1; mux's little show-off thing there is a proof. QED. Bingo. Smashy.
Svensta	Date: August 5, 2005 @ 8:08 AM the limit as r approaches 1? That's the thing about approaching. It never ACTUALLY gets there. Meaning it does not precisely equal 1, ever.
DaveWL	Date: August 5, 2005 @ 8:17 AM Mux, Halaka I know I am going to regret not letting this go, I ‘m still going to say it’s not 1 The fact that you can add the decimal equivalent of 3 thirds together and it comes to the number that is the subject of this forum is coincidence. I agree with Mux’s logic but I still think the value 9.999r can exist independently of being the sum of adding the decimal equivalent of a third together 3 times. The value 9.999r exists and is something slightly smaller than 1. If anybody understands what I just said – could they please explain it back to me. Oh yeah - what Svensta is saying is a good way of putting it.
sinai	Date: August 5, 2005 @ 8:26 AM anyone finished with 22/7 yet?
zedsalt	Date: August 5, 2005 @ 12:06 PM Mux's proof reflects the work of the great theortician, Midas Welby. Is 0.9r equal to 1? Midas Welby!
Apertome	Date: August 5, 2005 @ 12:07 PM Svensta -- the question has nothing to do with "the limit as r approaches 1." Nothing's approaching anything. 0.99999... is a constant. Limits/asmyptotes have to do with functions. Dave ... I don't understand how a number could exist independently of itself. 0.33333.... * 3 is clearly 0.99999.... since each digit gets multiplied by 3. When you multiply 1/3 by 3, there's no rounding necessary, because the answer is 1.
zedsalt	Date: August 5, 2005 @ 12:08 PM gurp! Forgot the other "e" in "theoretician"...
jd2theog	Date: August 5, 2005 @ 12:15 PM ^^Dave,svensta..I agree,.. 9.998 is not the same thing as 10.00 it's close, but it's just,9.998 just like 0.999r = 0.999r, it will always be 0.111r short of=1.0 sunai1,.. 3.1428571 (22/7) I tink thats right..its close to pi. (robert m had the jumbled ver)
zedsalt	Date: August 5, 2005 @ 12:36 PM I don't think it'd be 0.1r; wouldn't it be 0.0r1?
kingo	Date: August 5, 2005 @ 12:49 PM There'd never be a 1 at the end of that, zed. Because there's never end of 9s after the decimal in .9r. So 1 - .9r = 0.0r. Which is 0. DaveWL: let it go or not, what mux presented is an iron-clad proof, and when you're talking math that's all there is. .9r isn't similar to 1, it is another way of representing 1.
jd2theog	Date: August 5, 2005 @ 12:55 PM Im not good with mathematical problems, I forgot the (h) in think..... went to school with zed.
fu-dog	Date: August 5, 2005 @ 1:12 PM 0.9r = 1 True - If you want it to be. IE, if such rounding is necessary for some sort of design or application. False - If you require adherence to the laws of mathematics. Math is an agreed upon language of absolutes, but these absolutes are broken every day to maintain functionality. There's always rounding and error in every "Real World" application. Choose your own reality and diddle your numbers accordingly. (PS - Go analogue!)
kingo	Date: August 5, 2005 @ 1:20 PM uhm. Which laws of mathematics says that 0.9r 1? There are certainly none that I can find. Mathematically those ARE equal. Just exactly the same as 1/3 = .3r, and 1/9 = .1r, and 2/4 = 1/2 and 2/3 = 4/6. So unless you can find some mathematics that would disprove that 1/9 * 9 = 1, you can't say that .1r * 9 1.
kingo	Date: August 5, 2005 @ 1:21 PM shit. all my "does not equal" signs got eaten. How happy that makes that hole thing look. let me reword the last bit - unless you can find some mathematics to disprove that 1/9 * 9 = 1, you can't say that .1r * 9 does not equal 1.
sinai	Date: August 5, 2005 @ 2:05 PM although, it should be said...if it makes you happy thinking 2+2=5, then hey, happy counting hippie! more power to ya
Dizeazed	Date: August 5, 2005 @ 2:10 PM Let me just say... That I know what 2 + 2 is... and I'm happy at that! nobby:
Apertome	Date: August 5, 2005 @ 2:16 PM 2 + 2 = 5, for very large values of 2.
sinai	Date: August 5, 2005 @ 2:19 PM and god bless that!!
fanch-t	Date: August 5, 2005 @ 3:29 PM mux just killed me
shadowself	Date: August 5, 2005 @ 3:33 PM Oh. I thought I was supposed to find the value for r... I didn't know it meant recurring.
Apertome	Date: August 5, 2005 @ 4:10 PM here's a thing about it. http://mathforum.org/library/drmath/view/55746.html
Snoogans775	Date: August 5, 2005 @ 5:13 PM yeah, it is quite different to deal with an infinite. I think that's one of the easiest things to work with once you're comfortable with some of the approaches to infinites though. so if you're so clever Sinai, give me your fantastic crazy math stinker on why 22/7 isn't=3.142857r !
Snoogans775	Date: August 5, 2005 @ 5:14 PM damn, I think I see a connection here, and if I'm right, than my statement just before my answer sure makes me look like a doofus
imemine	Date: August 5, 2005 @ 8:58 PM Damn! I missed the best parts of this---Mux is right! I use Enron math.
shadowself	Date: August 5, 2005 @ 9:04 PM I work for an ISP. Our accounting server is named Anderson.
Veracohr	Date: August 6, 2005 @ 12:01 AM Nerds. I'm gonna go play D&D.
evansorchid	Date: August 6, 2005 @ 12:16 AM This entire forum discussion reminds me of the logic as explained in the movie..'This Is Spinal Tap'...where the guitarist explains that his amplifier knobs don't go to 10 for the maximum volume, but in fact the amplifier knobs go to 11... I need to get me some of those knobs.
imemine	Date: August 6, 2005 @ 1:27 AM ....but this one goes to eleven!
egac	Date: August 6, 2005 @ 2:57 AM 1=2
egac	Date: August 6, 2005 @ 3:04 AM Proof: say x=y x^2 = xy x^2 + y^2 = x^2 + xy 2x^2 = x^2 + xy 2x^2 - 2xy = xy - 2xy 2x^2 - 2xy = x^2 + xy - 2xy 2x^2 - 2xy = x^2 - xy 2(x^2 - xy) = (x^2 - xy) 2=1
jd2theog	Date: August 6, 2005 @ 3:13 AM its like 1 louder than 10. kinda like 10.999999r I can learn something Never thought I'd be learning math at DMusic.
Snoogans775	Date: August 6, 2005 @ 5:42 AM fuck it x=x and that's all there is to it, and if x=1 and x=2, I'm not satisfied unless the divine creature living just between this universe and the next convinces me, have you got the cajones to take that responsibility egac?
kingo	Date: August 6, 2005 @ 9:06 AM egac, you just divided by zero, which you can't do. to get from 2(x^2 - xy) = (x^2 - xy) to 2 = 1, you have to divide both sides by (x^2 - xy), but you can't do that because x^2 - xy is 0 (as x^2 = xy, so x^2 - xy = xy - xy, so you divded both sides by xy - xy.) This is why I was hiding on your page. I knew you were up to something.
Snoogans775	Date: August 7, 2005 @ 4:39 AM whoa, I believe you just got crowned "Transdimensional Super-Being"!
kingo	Date: August 7, 2005 @ 11:35 AM It's about fuckin' time.
zedsalt	Date: August 7, 2005 @ 12:02 PM No wonder I've never been up for that title! I didn't know mathematics were involved. I wish I could do a good impression of Chevy Chase's bad impression of Gerald Ford... "I was under the impression there would be no math".
pancreaspuppet	Date: August 8, 2005 @ 5:41 AM I think mux nailed it... That's a fucking awesome question, though, man. It's still boggling my mind.
pog	Date: August 8, 2005 @ 7:17 AM 0.3r is not the same as 0.333x where x is a finite number, so if you were to multiply 0.3r by 3, you would get 1. However 0.9r is not the same as 1 or 0.3r *3 In short, the answer to the original question is no 0.9r does not equal 1... but it's pretty close. 3.142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857 is as far as I can get for sinai's question.
Intergalacti...	Date: August 8, 2005 @ 7:47 AM Yes but isn't 0.3r exactly a third? Thats how I've always learned it. Lets move onto what mux said that 2+2 does=5 because that sort of related to the same procedure. Imagine 2 being 2.49999r surely thats close enough to 2.5 to round it up so if we added those two together it would actually be 5?
Svensta	Date: August 8, 2005 @ 8:11 AM Notice the normal thread wh0res are missing from this one? Oh and this CAN be viewed as a limit problem, Mux. Simply because .9999 is closer than .999. As you add nine's onto the end of the equation (as you work to positively solve the problem through simple math) you continually draw closer and closer to the eventuality of 1. So as you get to .9999999, you still have to solve to .99999999, which means you ARE approaching 1.
DaveWL	Date: August 8, 2005 @ 8:26 AM I’m coming around to thinking they are the same number. Pog is rejecting that (3 * 0.3r) = 0.9r which is fundamental to Mux’s logic. Is it actually possible to do multiplication on recurring numbers? – for instance what is (4 * 0.3r) I’m not sure that can be done. But I think (3 * 0.3r) is 0.9r because every 3 will always become a 9. Svensta, although I agreed with your “approaching” concept initially I don’t now. You refer to it like it’s a moving calculation, as if the number gets bigger as your looking at it – but the number always has an infinite number of 9s, it’s a constant as Mux says. I don’t think there are any anomalies in mathematics but I think there are anomalies with the decimal system and this is why we can get 2 expressions of the same value. I will probably change my mind tomorrow as puppet says this is mind boggling.
kingo	Date: August 8, 2005 @ 8:45 AM 4 * 0.3r = 4 * 1/3 = 4/3 4/3 = 1 + 1/3 1 + 1/3 = 1.3r So just divide 4 by 3 and you have your answer there, DaveWL. Yes, it's possible to multiply recurring decimals.
Svensta	Date: August 8, 2005 @ 9:22 AM Perhaps the real problem is that .333333 etc is really an inaccurate notation for a third.
kingo	Date: August 8, 2005 @ 9:30 AM I don't think it's inaccurate. I think it's just being misrepresented a lot here. I think it needs to get itself a good lawyer.
wailingmiserere	Date: August 8, 2005 @ 9:43 AM I'm losing sleep over this one
wailingmiserere	Date: August 8, 2005 @ 9:50 AM From the page mux posted: "0.999999... doesn't fall short of 1 _until_ you stop expanding it. But you never stop expanding it, so it never falls short of 1." Hmmm. Sort of makes sense It has always interested me that humans are capable of coming up with concepts like infinity and imaginary numbers, yet find these concepts almost impossible to imagine...
wailingmiserere	Date: August 8, 2005 @ 9:54 AM Maybe this is a confusing question because we're used to thinking of things as infinitely big... whereas the gap between 0.999...r and 1 is infinitely small.
ChillinBuzz	Date: August 8, 2005 @ 9:56 AM infinity... its a big number, no?
wailingmiserere	Date: August 8, 2005 @ 10:00 AM or a very, very small one
Apertome	Date: August 8, 2005 @ 11:34 AM I was going to let Svensta's logic go, but then I didn't. He said: "Simply because .9999 is closer than .999. As you add nine's onto the end of the equation (as you work to positively solve the problem through simple math) you continually draw closer and closer to the eventuality of 1." No, again, here you're referring to it as an "equation," but that's not what we're talking about. It's a constant. Constants don't approach anything. They are what they are. There is no "eventuality of 1," the number EQUALS one, as the proof above shows. The problem here is that 0.9999... repeats INFINITELY. You really can't break it up into bite-sized chunks like you're doing, unless you are very careful to remember that it never stops repeating. Someone else said the difference between 0.9r and 1 is 0.0r1 -- which makes sense, but 0.0r1 is meaningless. There'll never be a 1, it's all zeroes. Now, the idea that 0.3r is not exactly equal to 1/3 ... what are you smoking? Work it out on paper if you don't believe it (obviously a calculator is uesless for this exercise)
Apertome	Date: August 8, 2005 @ 11:35 AM useless too!
zedsalt	Date: August 8, 2005 @ 12:34 PM I beg patience from all of those here who actually know what they're talking about, but how can one recognize 0.9r as a quantity WITHOUT acknowledging the existence of a quantity equal to a one preceded by an infinite number of zeros? I mean, I understand what you're saying about it not being a truly infinite number of zeros if the one can ever be reached, but couldn't the same argument be made against 0.9r as a quantity? If a quantity of one preceded by an infinite number of zeros cannot exist, how can a quantity of 0.9r? Again, I'm not disagreeing so much as asking for clarification to cure the kind of psychalgic insomnia wailingmiserere mentioned.
kingo	Date: August 8, 2005 @ 12:52 PM One of the problems here is that there's a level jump going on, between pure mathematics and philosophy, or something like it. I think. 0.7r, 0.9r, 0.8r, 0.13r, (all using this new, weird notation where "r" just means that all of the preceding digits after the decimal point repeat, which is normally represented by a little bar over the repeating digits,) are all just representations of mathematical concepts. They don't inherently MEAN anything; they aren't inaccurate, they're just symbols. 1 - .9r is 0. It's not almost sort of zero but really a decimal point followed by a bunch of zeroes followed somewhere after infinity by a 1. That's all gibberish. We use mathematical notation to represent concepts so we can communicate mathematical things. For example, to represent a one one-thousandth, we could write .001, or we could write 1x10^-3. Neither representation's any more or less accurate; they're both just groups of symbols that mean something because we say they mean something. .3r IS 1/3 3 x 1/3 IS 1 3 x .3r IS 1 3 x .3r IS .9r .9r IS 1 Equality in mathematics is straightforward. It's not talking about metaphors; it means what it means. And now more specifically, Zed -- there's no quantity of a decimal point followed by an infinite number of zeroes followed by a 1 because that doesn't MEAN anything. There's no mathematical thing that represents, EXCEPT, if we want to coin some coins here, to say that that IS 0. So we can just say 0.0r1 is a way to represent 0, and we could do that to have a more pallatable (for people who are looking for such a thing) answer to the question of what 1 - .9r is. 1 - .9r = .0r1 But without giving it a meaning, it doesn't have ANY inherent meaning. Hope this clears anything up.
Apertome	Date: August 8, 2005 @ 12:53 PM A thing can go on forever; however, something can't happen AFTER something has gone on forever. There's no problem with having a decimal point followed by an infinte number of 9s (or any other number). But to say it's followed by an infinite number of 0s and then a one ... just doesn't make sense, because by definition something that's infinite never ends.
2step-4eva	Date: August 8, 2005 @ 1:02 PM i think u all missed the real equation that proves 0.9r=1...if i can remember it from GCSE maths... x=0.99999r therefore 10x=9.99999r 9x=10x-9x,=9.99999r-0.99999r,=9 9x=9 therefore x=1 therefore 0.99999r=1
kingo	Date: August 8, 2005 @ 1:18 PM That's another valid equation... though it's not the "real" equation. except where you said 9x = 10x - 9x you meant 9x = 10x - x, I think.
just2ska	Date: August 8, 2005 @ 1:36 PM DOES 3 = 2 ? NOW... DOES .9r = 1 ? YOU'RE WELCOME.
wailingmiserere	Date: August 8, 2005 @ 4:19 PM What do you subtract from 1 to get 0.9999... ? Hmm?
wailingmiserere	Date: August 8, 2005 @ 4:20 PM Can't be done, because, as already discussed, you can't have a decimal point followed by an infinite number of zeros and THEN a one because then the zeros wouldn't be infinite.
wailingmiserere	Date: August 8, 2005 @ 4:21 PM Same number. YOU'RE WELCOME.
pog	Date: August 8, 2005 @ 5:09 PM Again, I say that 0.9r is not equal to 1. and 0.333 with a finite number of reocurring digits is not exactly 1/3. It's like saying about half an apple is half an apple when if you measure it, it's in fact ... close enough.
Apertome	Date: August 8, 2005 @ 5:28 PM That's the point, Pog, we're talking about infinite repeating digits, not finite ones.
Jesuszilla	Date: August 8, 2005 @ 6:05 PM This thread seems to pop up every year on every forum in the world. It never ends!
shadowself	Date: August 8, 2005 @ 6:39 PM I have been out of school for a while. The "r"... is this the standard way of indicating a repeating number? How does it keep from getting mixed up in an algebra equation that has r as a variable? I recall putting a line over the repeating number.
pog	Date: August 8, 2005 @ 7:30 PM if you can draw a line over a digit in this forum, the please do, but for the benefit of this debate, I'm gonna use an r so if we're talking about infinite reoccuring numbers you have to agree that 3 * 0.3r can't possibly be the same as 0.9r simply because the 0.0000r1 can't have vanished.
Snoogans775	Date: August 8, 2005 @ 7:33 PM normally the decimal has a little bar over it like that if that comes up. ____ 0.9999
pog	Date: August 8, 2005 @ 7:58 PM ___ 0.999
kingo	Date: August 8, 2005 @ 8:07 PM Pog, dude... you just trying to goad us, or what? If you could offer any kind of mathematical proof for that statement I'd appreciate seeing it.
pog	Date: August 9, 2005 @ 4:52 AM Well, yes and no... It's a paradox.... I believe that both equations are correct as mathematical possiblities. Here's the same discussion that comes to the conclusion that I had. http://forums.ugo.com/archive/index.php/t-20616.html
mattbanx	Date: August 9, 2005 @ 4:57 AM Value of pie. Yeah, there is no real equation. I think I found that out on a Star Trek episode before the math teacher told me.
mattbanx	Date: August 9, 2005 @ 4:58 AM I add, I am the furthest think from a mathmatician.
DaveWL	Date: August 9, 2005 @ 5:35 AM I think part of the problem is that the decimal system is not good for handling certain values. If we had base 12 at the centre of our numerical system then it would be easier to represent a third but we would still have problems with other numbers We have always grouped things in 10s (and 5s) since ancient times because of the number of fingers we have. So that’s why we have the decimal system. When it came round to developing a system for measuring angles, 360 was chosen because it was divisible by so many numbers. Just a word with the Pi thing. The circle and sphere is the most perfect and natural form in nature. So why is there such a strange number at the heart of it’s construction. Shouldn’t it be something perfect and rounded too. I’m sure if someone could get to the bottom of that we’d find the answer to the great mysteries of creation itself….or maybe not.
wailingmiserere	Date: August 9, 2005 @ 6:34 AM It's interesting the way that humans attempt to approximate things which are perfect... we are imperfect and can only see things from a certain biased viewpoint. We have to reduce concepts to levels that our small minds can handle. But speaking in strict mathematical terms, 0.999... does equal 1. It doesn't make much sense to me in a physical sense, but mathematically it is true. Rather like the square root of -1.
wailingmiserere	Date: August 9, 2005 @ 6:41 AM Maybe somewhere in the universe there are aliens with pi number of fingers on each hand and they've got the meaning of life all figured out already...
mattbanx	Date: August 9, 2005 @ 7:04 AM Hell, if we can figure that out, maybe we will reach that level.
Alecs	Date: August 9, 2005 @ 9:59 AM if you put a .99 inch piece of string in a box of 1 inch pieces of string, nobody would notice the .99 inch piece of string. Though they are not tecnichally equivelant, it's a really small difference.
kingo	Date: August 9, 2005 @ 11:01 AM yes, but if you put a .9repeating piece of string in a box of 1 inch pieces of string, all the pieces of string would be 1 inch still.
zedsalt	Date: August 9, 2005 @ 12:16 PM I have three people nearby...well, kind of nearby...who I'd like to run this past. I spoke to one last night/early this morning. As soon as I mentioned the equation, he interrupted by saying, "Um hmm! One of the equations that proves 'NX=Z, and YX=Z, therefore N=Y' is by NO means an absolute property! Here are a few more..." He then flipped over a paper placemat and proceeded to scribble out three equations that he claimed...convincingly enough for a novice like me...were exceptions to that property. Apparently, it is a "-sophy" rather than an "-ology" kind of question, and not one everyone agrees upon.
kingo	Date: August 9, 2005 @ 1:07 PM I'd definitely be interested in seeing those instances where NX = Z, YX = Z, and N does not equal Y. One instance is if either X or Z is zero. If X is zero, then N*X = Z will be true for any N if Z is also zero. Beyond that there may be more; I'm not prepared to make any categorical statement about that vague couple of equations. What I am prepared to do, however, is to say that the original proof that mux offered is mathematically sufficient to prove that .9repeating = 1 within our mathematical system. This isn't really a debatable thing. You can say, "well, I don't accept our mathematical system as being accurate," sure. Here are a lot of proofs: http://www.answers.com/topic/proof-that-0-999-equals-1
Intergalacti...	Date: August 10, 2005 @ 4:22 PM Holy hell I have unleashed a monster To work out this equation wouldn't we have to find out how many the word 'infinite' means. Surely if .9r meant that the nine was gettin smaller and smaller would we sometime have to end up going backwards because its getting to close to one?
kingo	Date: August 10, 2005 @ 4:54 PM Man, somebody lock this thread before my fucking potato explodes.
GeneHilbert	Date: August 11, 2005 @ 1:09 AM I'm actually enjoying this ...... Kind of
wailingmiserere	Date: August 11, 2005 @ 4:27 AM But it isn't getting smaller and smaller. It's a constant number. Infinite doesn't mean 'how many.' It's a meaningless concept that no one can understand. The easiest way to get your around it, I think, is the 1/3 * 3 thing. I wasn't sure about this at first, because I was thinking that 0.333... is only an approximation of 1/3. But it is exact, as long as the 3s go on infinitely. In the same way that 0.999... is exactly 3/3 = 1 as long as the 9s are infinite. Perhaps it's easier to think of it as a symbol for 1, rather than a number. It's just an oddity of the decimal system.
leplume	Date: August 11, 2005 @ 7:35