Members thinkpad20 Posted October 11, 2009 Members Share Posted October 11, 2009 let's make this simple. the OP states .999_ = 1 0.999... does not equal 1.0 no matter how you think about, put it, calculate it it gets close but does not equal 1.0 Yes it does. There have already been about 4 or 5 proofs/demonstrations that show this.It seems your flaw of thinking is that with 0.9999.... the 9s end at some point. Well they don't. They keep on going for infinity. If they did end at some point, then yes, you could say "it gets close but does not equal 1." But since they never end, it is equal to 1.Look, no one ever said that it would be easy.... Quote Link to comment Share on other sites More sharing options...
Members Chippy Posted October 11, 2009 Members Share Posted October 11, 2009 Yes it does. There have already been about 4 or 5 proofs/demonstrations that show this. It seems your flaw of thinking is that with 0.9999.... the 9s end at some point. Well they don't. They keep on going for infinity. If they did end at some point, then yes, you could say "it gets close but does not equal 1." But since they never end, it is equal to 1. Look, no one ever said that it would be easy.... No, it doesn't. It's as close as you can possibly get to 1 without actually getting 1. Also, whoever posted 9/9 = .999... is an idiot.Morons. Quote Link to comment Share on other sites More sharing options...
Members Uncle_Milton Posted October 12, 2009 Members Share Posted October 12, 2009 Yes it does. There have already been about 4 or 5 proofs/demonstrations that show this. It seems your flaw of thinking is that with 0.9999.... the 9s end at some point. Well they don't. They keep on going for infinity. If they did end at some point, then yes, you could say "it gets close but does not equal 1." But since they never end, it is equal to 1. Look, no one ever said that it would be easy.... But there is an infinite number of real numbers between 1.0 and 0.9999... Quote Link to comment Share on other sites More sharing options...
Members Marshredder Posted October 12, 2009 Members Share Posted October 12, 2009 The difference between 0.999... and 1 is 0.111... Quote Link to comment Share on other sites More sharing options...
Members thinkpad20 Posted October 12, 2009 Members Share Posted October 12, 2009 No, it doesn't. It's as close as you can possibly get to 1 without actually getting 1. Also, whoever posted 9/9 = .999... is an idiot. Morons. Nope; you're wrong. Look, I don't know what to say. Go up and read some of the 5 or so proofs that have already been shown. As long as the 9's go on for infinity, it is equal to one. End of story. There's no discussion to be had really; this is just math. If you don't understand it, it's likely just that you haven't learned about infinite sums or limits or whatnot. Or you've forgotten what you had learned. Quote Link to comment Share on other sites More sharing options...
Members dreamspace Posted October 12, 2009 Members Share Posted October 12, 2009 This topic is the math worlds equvilant to the guitar worlds "TOANZ IS IN THE FINGERS, TRUE/FALSE?" question. It's been discussed to DEATH and back, for many many MANY years. Quote Link to comment Share on other sites More sharing options...
Members Mattie Posted October 12, 2009 Members Share Posted October 12, 2009 But there is an infinite number of real numbers between 1.0 and 0.9999... No, There are 0 amount of real numbers between 1.0 and .999... Quote Link to comment Share on other sites More sharing options...
Members Uncle_Milton Posted October 12, 2009 Members Share Posted October 12, 2009 Not if I start writing my set first:poke: Quote Link to comment Share on other sites More sharing options...
Members JKD Posted October 12, 2009 Members Share Posted October 12, 2009 It was Zeno.I'd hand him an introductory calculus text and let him work it out for himself. I argued this one with my Physics teacher...told him his statement of the problem was wrong....in the real world, the 'other side of the coliseum' is an arbitrary limit on the distance travelled...he was having none of it..and basically said the example illustrates the point he was trying to get across about calculus...he tried to pull the same {censored} about the tortoise never being able to catch the hare...pfft. Quote Link to comment Share on other sites More sharing options...
Members sled Posted October 12, 2009 Members Share Posted October 12, 2009 Yes it does. There have already been about 4 or 5 proofs/demonstrations that show this. It seems your flaw of thinking is that with 0.9999.... the 9s end at some point. Well they don't. They keep on going for infinity. If they did end at some point, then yes, you could say "it gets close but does not equal 1." But since they never end, it is equal to 1. Look, no one ever said that it would be easy.... no. .999... approaches 1.0 but never reaches 1.0. there will always be an infinitesimal difference. always. Quote Link to comment Share on other sites More sharing options...
Members mamberg Posted October 12, 2009 Members Share Posted October 12, 2009 I argued this one with my Physics teacher...told him his statement of the problem was wrong....in the real world, the 'other side of the coliseum' is an arbitrary limit on the distance travelled...he was having none of it..and basically said the example illustrates the point he was trying to get across about calculus...he tried to pull the same {censored} about the tortoise never being able to catch the hare...pfft.I agree with you - what if the coliseum were only 1/2 as big?Then the first assumption that you first have to cross the first half, would put you all the way across!!I realize I'm arguing both sides of MY argument............ Quote Link to comment Share on other sites More sharing options...
Members thinkpad20 Posted October 12, 2009 Members Share Posted October 12, 2009 no. .999... approaches 1.0 but never reaches 1.0. there will always be an infinitesimal difference. always.Sigh. You clearly just don't know what you're talking about. The matter is resolved... Quote Link to comment Share on other sites More sharing options...
Members sled Posted October 12, 2009 Members Share Posted October 12, 2009 Sigh. You clearly just don't know what you're talking about. The matter is resolved...you are answering a different question of convergence. as terms are added to the series representing .999..., the function converges to 1.0, but that is not the same thing as stating .999... = 1.0convergence is about finite limits. this is a mathematical requirement, else one could never solve a problem of distance as one object aproaches another because the distance is always halved, but obviously the distance between the two objects does approach Zero. convergence is a rule of necessity and of finite possibilities. that's not the case with .999... in this case, the number .999... will always have an infinitesimal difference with 1.0. Quote Link to comment Share on other sites More sharing options...
Members Captain Commie Posted October 12, 2009 Members Share Posted October 12, 2009 Sigh. You clearly just don't know what you're talking about. The matter is resolved...seconded Quote Link to comment Share on other sites More sharing options...
Members extollo Posted October 12, 2009 Members Share Posted October 12, 2009 no. .999... approaches 1.0 but never reaches 1.0. there will always be an infinitesimal difference. always.are you thinking that the 9's literally repeat over time? there are always infinite 9s. remember .333... is equal to 1/3 Quote Link to comment Share on other sites More sharing options...
Members sled Posted October 12, 2009 Members Share Posted October 12, 2009 are you thinking that the 9's literally repeat over time? there are always infinite 9s. remember .333... is equal to 1/3 .999... indicates an infinite number of terms in the series and yes the as the number of terms approaches infinity, .999... converges to 1.0, but this is not the same thing as stating .999... = 1.0 Quote Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted October 12, 2009 Members Share Posted October 12, 2009 .999... indicates an infinite number of terms in the series and yes the as the number of terms approaches infinity, .999... converges to 1.0, but this is not the same thing as stating .999... = 1.0This. Thank you. Quote Link to comment Share on other sites More sharing options...
Members Uncle_Milton Posted October 12, 2009 Members Share Posted October 12, 2009 remember .333... is equal to 1/3Or is it not, but functionally defined as such? Quote Link to comment Share on other sites More sharing options...
Members satannica Posted October 12, 2009 Members Share Posted October 12, 2009 LMFAO! This thread is fantastic! Quote Link to comment Share on other sites More sharing options...
Members MadKeithV Posted October 12, 2009 Members Share Posted October 12, 2009 LMFAO! This thread is fantastic! Yeah, it is Reminds me of a discussion about compression on another forum (the zip kind, not the audio kind). With someone repeatedly claiming they could beat information theory all the time, in the general case... Quote Link to comment Share on other sites More sharing options...
Members RoboPimp Posted October 12, 2009 Members Share Posted October 12, 2009 brewtal Quote Link to comment Share on other sites More sharing options...
Members satannica Posted October 12, 2009 Members Share Posted October 12, 2009 That's the thing about the internet... it's brought together a lot of people with a complete contemptable lack of real education manifested in lots of blah blah woof woof about things they would like to think they know about but don't really. I blame discovery channel and liberals! Quote Link to comment Share on other sites More sharing options...
Members mparsons Posted October 12, 2009 Members Share Posted October 12, 2009 .999... indicates an infinite number of terms in the series and yes the as the number of terms approaches infinity, .999... converges to 1.0, but this is not the same thing as stating .999... = 1.0This does not occur over time. There is no "approaching" here. If we were talking of a series such as .9, .99, .999, .99999999999999999999, .99999999999999999999999999999999999999999999, you would be correct, but .999... represents those 9s extending into infinity, in the present, right now, forever.Thus equaling 1, by your own admission. Quote Link to comment Share on other sites More sharing options...
Members Jesse G Posted October 12, 2009 Members Share Posted October 12, 2009 This does not occur over time. There is no "approaching" here. If we were talking of a series such as .9, .99, .999, .99999999999999999999, .99999999999999999999999999999999999999999999, you would be correct, but .999... represents those 9s extending into infinity, in the present, right now, forever. Thus equaling 1, by your own admission. .999_ is less than 1 by an infinitely small difference, but a difference nonetheless. Quote Link to comment Share on other sites More sharing options...
Members MeshigganeH Posted October 12, 2009 Members Share Posted October 12, 2009 . LoL ohhh kids these days... +1. Quote Link to comment Share on other sites More sharing options...
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