Posted September 24, 2005 I'm having a mathematical debate with someone who believes 1 = 0.9999... I personally, do not think that this is the case, even with his really terribly smart (for 14) equations: -------------------- Let X = 0.999... • Then 10X = 9.999... Subtract X from each side to give us: • 9X = 9.999... - X but we know that X is 0.999..., so: • 9X = 9.999... - 0.999... or: • 9X = 9 Divide both sides by 9: • X = 1 -------------------- x = 0.9999... n=N := lim Σ 9·10-n N→∞ n=1 = lim ( 1 - 10-N ) N→∞ = lim 1 - lim 10-N N→∞ N→∞ = 1 - 0 = 1 -------------------- 0.9999... ≤ 1 If 0.9999... < 1 then there is some positive number P so that 0.9999... + P = 1 But for ANY positive P, 0.9999... + P > 1 which contradicts the equation in . Therefore the only possible alternative is 0.9999... = 1 -------------------- Buw how can 1 = 0.99999999... HELP PLEASE! Share this post Link to post Share on other sites
Posted September 24, 2005 I guess it has no solution Share this post Link to post Share on other sites
Posted September 24, 2005 This argument is as old as the sun. What they mean is 0.99999999... = 1. Not 1 = 0.99999999. Then the line gets blurry. You have an infinitely close value to 1, but you never quite have 1. Either way don't ask me. Don't argue about this though, it's a waste of time. Share this post Link to post Share on other sites
Posted September 24, 2005 But since, as you say, never quite 1, then how can it equal 1?! Share this post Link to post Share on other sites
Posted September 24, 2005 oh dear god, not this, please... SA gets this so much they've made it a bannable offence to start up this discussion ¬_¬ Share this post Link to post Share on other sites
Posted September 24, 2005 Really? I've never seen it anywher ebefore on the net, ever. Share this post Link to post Share on other sites
Posted September 24, 2005 One equals one. If your friend thinks otherwise just let him believe that. The mathematical equations that you posted are incorrect. Share this post Link to post Share on other sites
Posted September 24, 2005 Basically, I think, everybody agrees 0.3333...=1/3, now multiply both sides by 3 1/3 x 3=1 0.3333... x 3=0.9999.... Therefore 0.9999...=1 Ah, I'm so clever Share this post Link to post Share on other sites
Posted September 24, 2005 You don't really get around that much... I search for it on the Something Awful forums (the 5th most active forum on the Internet, apparently) and it comes up many a time, with people oft-groaning from its resurrection. Share this post Link to post Share on other sites
Posted September 24, 2005 You don't really get around that much... I search for it on the Something Awful forums (the 5th most active forum on the Internet, apparently) and it comes up many a time, with people oft-groaning from its resurrection. what are the 4 more active forums? Share this post Link to post Share on other sites
Posted September 24, 2005 I dunno man, I don't remember at all... That's the only statistic I could remember from whereever I saw it. Either way it's the #1 for just being the awesome on the internet. Share this post Link to post Share on other sites
Posted September 24, 2005 I was about to post Monopolyman's solution, but he beat me to it. Anyway, most mathematical people (ie. my teachers) seem to think that 0.9999... is equal to 1, and I believe some exam papers (I've definitely tried some practice papers where this is the case) require that you will assume this in order to get the right answer to the question. Share this post Link to post Share on other sites
Posted September 25, 2005 1 only equals 0.999rec if you assume 1/3 = 0.333rec. But how then can you equally divide 1 by 3 AND 4? If you work in 1/3rds, sure, 1 does equally 0.999rec. But that is NOT an exact measurement. The increment is so slight that it cannot be exactly measured, as 1 is not equally divisible by 3, much like 10 isn't. If you assume 1/4 of 1 is is 0.25 then 1 equals 1. 1 is 1, not 0.999rec. Saying that 1 = 0.999 is a contradiction in itself because they are two different numbers. Share this post Link to post Share on other sites
Posted September 25, 2005 Basically, I think, everybody agrees 0.3333...=1/3, now multiply both sides by 3 1/3 x 3=1 0.3333... x 3=0.9999.... Therefore 0.9999...=1 Ah, I'm so clever What 1/3 doesn't equal 0.3333, it's just easy and normall currect to assume it equals 0.3 reacoricing for an invinte times, but it real terms of mathmatics you can't put 1/3 as a unit ither wise 1 would have to equal 0.9999 reacuring. arrr i hate maths anyway. Share this post Link to post Share on other sites
Posted September 25, 2005 the line of working that looks dodgy to me is. 9X = 9.999... - 0.999... 9*0.99999....rec does not equal 9.999.....rec does it? to me it sounds wrong. Surely at the end you will get a small bit of difference. The only way this would be true is if you did 10*0.9999rec Therefore, the step where you took away 0.999 to leave 9 is wrong. It would infact leave a tiny bit left. 0.0000001 or something. therefore the whole rest of the proof does not work. Share this post Link to post Share on other sites
Posted September 25, 2005 0.99999 = 1 because it is rounded Share this post Link to post Share on other sites
Posted September 25, 2005 I'm not too good at the old mathematical equations but I worked this out... 3-2 = 1 Share this post Link to post Share on other sites
Posted September 25, 2005 how the hell you came up with that i dont know, 1 is 1, its like saying, a person is a monkey. well its not but if someone says 1 then thats what it is. But then again i dont know that much about maths... Share this post Link to post Share on other sites
Posted September 25, 2005 This is wher emy confusion set in aswell Zakatu. .99999rec x 9 = 8.999rec1 But .99999rec x 10 - .9999rec = 9 Very odd.... Share this post Link to post Share on other sites
Posted September 25, 2005 ..I think there's several more possibilities than the 0.9999..= 1 thing (if I can remember correctly) because our maths teacher in my last year at school showed us stuff like that near the end of term with a few different numbers.. but the number's had to end with 9s or something.. Share this post Link to post Share on other sites
Posted September 25, 2005 ah, god. I've had a rethink and it seems to be mathematically right. I can't seen any errors in the working. I think where the error lies (and there has to be one) is in an assumption made. It seems small but 0.99999rec * 10 perhaps does not equal exactly 9.999999 rec because you have shifted everything one place forward, so what ever "inaccuracy" there is at infinite places has now become 10* bigger. so assuming that 9.99999rec is the same as 10*0.999999 might be the downfall behind this. However, i'm not very good at proofs and am probably wrong, because to me it seems mathematically right. I think to solve this perhaps its all about the nature of infinite and what a recurring number actually is...definitions. because tbh, there isn't any REAL difference between 9.999999 rec and 10. nothing that you can right down is there? but we do know they are not the same. Share this post Link to post Share on other sites
Posted September 25, 2005 it is way too early for things like this :P dabookerman comes up with a simple theory so im going with that Share this post Link to post Share on other sites
Posted September 25, 2005 Dabookerman is wrong; it's not rounded, it simply is 1. With each 9 added, it gets closer to 1. You have to stop writing it out somewhere, as it is recurring and you would run out of space. At the point where you stop writing, it isn't equal to 1, but taken as a whole, the number is. And 0.333rec isn't an approximation of 1/3- try dividing 1 by 3 with long division and see what comes out. This means that this proof does work, and although I personally think it is the neatest, the others work too. Share this post Link to post Share on other sites
Posted September 25, 2005 Dabookerman is wrong; it's not rounded, it simply is 1. It isn't one, 0.9999 recurring is not 1. its the closest it can be without being one, but it isn't 1. The proof makes out that it IS exactly one, i think the proof is wrong somewhere. Share this post Link to post Share on other sites
Posted September 25, 2005 you really are a funny old bunch on this forum Share this post Link to post Share on other sites
