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 Posts: 5,316 Add as FriendChallenge to a DebateSend a Message 5/11/2014 12:25:58 PMPosted: 3 years agoAt 5/11/2014 11:23:25 AM, PeacefulChaos wrote:1. The infinite series of 1/2, 1/4, 1/8 ... should theoretically add up to 1, but isn't the reality that it will only get infinitesimally close to 1? So, in order for the refutation to Zeno's paradox to be valid, would we not have to accept that 0.999...= 1? Certainly, there have been arguments for this; however, I've observed multiple debates in which PotBelliedGeek manages to demonstrate that 0.999... = / = 1.http://www.debate.org...If there would be any refutations to his arguments, I'd gladly like to hear them.1) The error is just ludicrous. PBG says "1-0.9... = 0.1..." which is just flat out wrong. The elipsis clearly referred to more of the previous digit. So that means, by PBG's estimation, 1-0.999... = 0.111 ... which is false.2) He claims that 1/3 is an approximation of 0.333... which is again false. The BoP would be to show this, but ultimately we know that this is not an approximation but true. 0.333... is equal to 1/3, as we can show with simple (or bus-stop) division.3) the concept you have to "add a zero to the right" is very interesting, but just false. As it is an infinite series, you do not have an "end" to put the 0 on. A novel response, but just not true.Give a man a fish, he'll eat for a day. Teach him how to be Gay, he'll positively influence the GDP. Social Contract Theory debate: http://www.debate.org...
 Posts: 2,767 Add as FriendChallenge to a DebateSend a Message 5/11/2014 12:43:18 PMPosted: 3 years agoEven if Achilles could reach the 1 distance (or x, or whatever it is), it wouldn't matter because by the time he got there, the tortoise will have moved ahead. So Achilles will never be able to catch it because every time he gets to where the tortoise was before, it will have moved ahead."Not to know of what things one should demand demonstration, and of what one should not, argues want of education." ~Aristotle "It is the mark of an educated mind to be able to entertain a thought without accepting it." ~Aristotle
 Posts: 13,034 Add as FriendChallenge to a DebateSend a Message 5/11/2014 1:16:45 PMPosted: 3 years agoThe paradox is resolved by acknowledging the fact that it is impossible to describe or define a change in any way that does not involve a sudden finite jump in some parameter."In case anyone hasn't noticed it, the West is in extremis. The undertaker is checking his watch at the foot of its bed, and there's a sinister kettle of croaking, money-feathered vultures on the roof."
 Posts: 13,034 Add as FriendChallenge to a DebateSend a Message 5/11/2014 1:24:28 PMPosted: 3 years agoThat is, a continuum is incompatible with the potential for change. Zeno's paradox relies on the assumption of both."In case anyone hasn't noticed it, the West is in extremis. The undertaker is checking his watch at the foot of its bed, and there's a sinister kettle of croaking, money-feathered vultures on the roof."
 Posts: 2,649 Add as FriendChallenge to a DebateSend a Message 5/11/2014 5:24:42 PMPosted: 3 years agoAt 5/11/2014 12:25:58 PM, Stephen_Hawkins wrote:At 5/11/2014 11:23:25 AM, PeacefulChaos wrote:1. The infinite series of 1/2, 1/4, 1/8 ... should theoretically add up to 1, but isn't the reality that it will only get infinitesimally close to 1? So, in order for the refutation to Zeno's paradox to be valid, would we not have to accept that 0.999...= 1? Certainly, there have been arguments for this; however, I've observed multiple debates in which PotBelliedGeek manages to demonstrate that 0.999... = / = 1.http://www.debate.org...If there would be any refutations to his arguments, I'd gladly like to hear them.1) The error is just ludicrous. PBG says "1-0.9... = 0.1..." which is just flat out wrong. The elipsis clearly referred to more of the previous digit. So that means, by PBG's estimation, 1-0.999... = 0.111 ... which is false.2) He claims that 1/3 is an approximation of 0.333... which is again false. The BoP would be to show this, but ultimately we know that this is not an approximation but true. 0.333... is equal to 1/3, as we can show with simple (or bus-stop) division.3) the concept you have to "add a zero to the right" is very interesting, but just false. As it is an infinite series, you do not have an "end" to put the 0 on. A novel response, but just not true.1. Yeah, I noticed that, too. I agree that is not a valid rebuttal.2. He provided a source, and I just skimmed over it, but I didn't find anything about 1/3 not being 0.3333.3. Okay. I also tried looking at the source he provided to back this up, but again I didn't find anything about it.Nevertheless, it seems odd that 0.999... = 1. After all, we can agree 0.9 isn't equal to one. We can agree 0.99 isn't equal to one. We can agree that 0.999...0 (the number of nines would be equal to the number of atoms on earth) isn't equal to one, and so on. Wouldn't this just be like a line approaching an asymptote? Even though it can get infinitesimally close to the line, it will never reach it.
 Posts: 2,649 Add as FriendChallenge to a DebateSend a Message 5/11/2014 5:28:15 PMPosted: 3 years agoAt 5/11/2014 12:46:42 PM, Envisage wrote:Remember, the distance is halved each time, and velocity remains constant. The time to reach each 'checkpoint' is also halved, and when you do the infinite series of each subdivision of time taken, the time taken is a finite quantity.Okay, but how does this explain the fact that Achilles is able to move across an infinite amount of "checkpoints?" I kind of see what you're saying, but it isn't exactly sticking. Regardless of time, it is impossible to move across an infinite number of points and go beyond that infinite number of points, isn't it?You could also think of it this way, the number of 'checkpoints' crossed each second increases inversely proportionally to the size of the checkpoints... and therefore cancel each other out.
 Posts: 2,649 Add as FriendChallenge to a DebateSend a Message 5/11/2014 5:32:42 PMPosted: 3 years agoAt 5/11/2014 1:16:45 PM, dylancatlow wrote:The paradox is resolved by acknowledging the fact that it is impossible to describe or define a change in any way that does not involve a sudden finite jump in some parameter.I'm not seeing how acknowledging that fact resolves the paradox. The only way it would resolve the paradox is if you accept that change is possible yet at the same time support the paradox. This would be a contradiction, and your arguments would fall apart.I believe, however, that Zeno argued that not only did motion not exist, but neither did change; thus, it is compatible with his views.
 Posts: 5,316 Add as FriendChallenge to a DebateSend a Message 5/11/2014 6:07:34 PMPosted: 3 years agoAt 5/11/2014 5:24:42 PM, PeacefulChaos wrote:At 5/11/2014 12:25:58 PM, Stephen_Hawkins wrote:At 5/11/2014 11:23:25 AM, PeacefulChaos wrote:1. The infinite series of 1/2, 1/4, 1/8 ... should theoretically add up to 1, but isn't the reality that it will only get infinitesimally close to 1? So, in order for the refutation to Zeno's paradox to be valid, would we not have to accept that 0.999...= 1? Certainly, there have been arguments for this; however, I've observed multiple debates in which PotBelliedGeek manages to demonstrate that 0.999... = / = 1.http://www.debate.org...If there would be any refutations to his arguments, I'd gladly like to hear them.1) The error is just ludicrous. PBG says "1-0.9... = 0.1..." which is just flat out wrong. The elipsis clearly referred to more of the previous digit. So that means, by PBG's estimation, 1-0.999... = 0.111 ... which is false.2) He claims that 1/3 is an approximation of 0.333... which is again false. The BoP would be to show this, but ultimately we know that this is not an approximation but true. 0.333... is equal to 1/3, as we can show with simple (or bus-stop) division.3) the concept you have to "add a zero to the right" is very interesting, but just false. As it is an infinite series, you do not have an "end" to put the 0 on. A novel response, but just not true.1. Yeah, I noticed that, too. I agree that is not a valid rebuttal.2. He provided a source, and I just skimmed over it, but I didn't find anything about 1/3 not being 0.3333.3. Okay. I also tried looking at the source he provided to back this up, but again I didn't find anything about it.Nevertheless, it seems odd that 0.999... = 1. After all, we can agree 0.9 isn't equal to one. We can agree 0.99 isn't equal to one. We can agree that 0.999...0 (the number of nines would be equal to the number of atoms on earth) isn't equal to one, and so on. Wouldn't this just be like a line approaching an asymptote? Even though it can get infinitesimally close to the line, it will never reach it.Consider it as a limit equivalent if you'd like. Ultimately, the two are equivalent though. It's just one of those things about how maths works - there are a lot of unintuitive things (like 1+2+3+4+... to infinity equals -1/12). Maths is deductive and not intuitive unfortunately.Give a man a fish, he'll eat for a day. Teach him how to be Gay, he'll positively influence the GDP. Social Contract Theory debate: http://www.debate.org...
 Posts: 13,034 Add as FriendChallenge to a DebateSend a Message 5/11/2014 6:36:10 PMPosted: 3 years agoAt 5/11/2014 6:07:34 PM, Stephen_Hawkins wrote:At 5/11/2014 5:24:42 PM, PeacefulChaos wrote:At 5/11/2014 12:25:58 PM, Stephen_Hawkins wrote:At 5/11/2014 11:23:25 AM, PeacefulChaos wrote:1. The infinite series of 1/2, 1/4, 1/8 ... should theoretically add up to 1, but isn't the reality that it will only get infinitesimally close to 1? So, in order for the refutation to Zeno's paradox to be valid, would we not have to accept that 0.999...= 1? Certainly, there have been arguments for this; however, I've observed multiple debates in which PotBelliedGeek manages to demonstrate that 0.999... = / = 1.http://www.debate.org...If there would be any refutations to his arguments, I'd gladly like to hear them.1) The error is just ludicrous. PBG says "1-0.9... = 0.1..." which is just flat out wrong. The elipsis clearly referred to more of the previous digit. So that means, by PBG's estimation, 1-0.999... = 0.111 ... which is false.2) He claims that 1/3 is an approximation of 0.333... which is again false. The BoP would be to show this, but ultimately we know that this is not an approximation but true. 0.333... is equal to 1/3, as we can show with simple (or bus-stop) division.3) the concept you have to "add a zero to the right" is very interesting, but just false. As it is an infinite series, you do not have an "end" to put the 0 on. A novel response, but just not true.1. Yeah, I noticed that, too. I agree that is not a valid rebuttal.2. He provided a source, and I just skimmed over it, but I didn't find anything about 1/3 not being 0.3333.3. Okay. I also tried looking at the source he provided to back this up, but again I didn't find anything about it.Nevertheless, it seems odd that 0.999... = 1. After all, we can agree 0.9 isn't equal to one. We can agree 0.99 isn't equal to one. We can agree that 0.999...0 (the number of nines would be equal to the number of atoms on earth) isn't equal to one, and so on. Wouldn't this just be like a line approaching an asymptote? Even though it can get infinitesimally close to the line, it will never reach it.(like 1+2+3+4+... to infinity equals -1/12).That's just fking bizarre lol"In case anyone hasn't noticed it, the West is in extremis. The undertaker is checking his watch at the foot of its bed, and there's a sinister kettle of croaking, money-feathered vultures on the roof."
 Posts: 2,649 Add as FriendChallenge to a DebateSend a Message 5/11/2014 6:44:58 PMPosted: 3 years agoAt 5/11/2014 6:07:34 PM, Stephen_Hawkins wrote:At 5/11/2014 5:24:42 PM, PeacefulChaos wrote:At 5/11/2014 12:25:58 PM, Stephen_Hawkins wrote:At 5/11/2014 11:23:25 AM, PeacefulChaos wrote:1. The infinite series of 1/2, 1/4, 1/8 ... should theoretically add up to 1, but isn't the reality that it will only get infinitesimally close to 1? So, in order for the refutation to Zeno's paradox to be valid, would we not have to accept that 0.999...= 1? Certainly, there have been arguments for this; however, I've observed multiple debates in which PotBelliedGeek manages to demonstrate that 0.999... = / = 1.http://www.debate.org...If there would be any refutations to his arguments, I'd gladly like to hear them.1) The error is just ludicrous. PBG says "1-0.9... = 0.1..." which is just flat out wrong. The elipsis clearly referred to more of the previous digit. So that means, by PBG's estimation, 1-0.999... = 0.111 ... which is false.2) He claims that 1/3 is an approximation of 0.333... which is again false. The BoP would be to show this, but ultimately we know that this is not an approximation but true. 0.333... is equal to 1/3, as we can show with simple (or bus-stop) division.3) the concept you have to "add a zero to the right" is very interesting, but just false. As it is an infinite series, you do not have an "end" to put the 0 on. A novel response, but just not true.1. Yeah, I noticed that, too. I agree that is not a valid rebuttal.2. He provided a source, and I just skimmed over it, but I didn't find anything about 1/3 not being 0.3333.3. Okay. I also tried looking at the source he provided to back this up, but again I didn't find anything about it.Nevertheless, it seems odd that 0.999... = 1. After all, we can agree 0.9 isn't equal to one. We can agree 0.99 isn't equal to one. We can agree that 0.999...0 (the number of nines would be equal to the number of atoms on earth) isn't equal to one, and so on. Wouldn't this just be like a line approaching an asymptote? Even though it can get infinitesimally close to the line, it will never reach it.Consider it as a limit equivalent if you'd like. Ultimately, the two are equivalent though. It's just one of those things about how maths works - there are a lot of unintuitive things (like 1+2+3+4+... to infinity equals -1/12). Maths is deductive and not intuitive unfortunately.Wait, what the ...Could you explain the 1 + 2 + 3 + 4 ... = -1/12?
 Posts: 5,000 Add as FriendChallenge to a DebateSend a Message 5/11/2014 7:14:22 PMPosted: 3 years agoWell obviously the paradox isn't sound considering that travel does not work that way in reality.I can travel from point A to point B even though I must first travel the infinite number of fractions between the two points.You see, if I travel half the distance between A and B I must not first travel 1/4, 1/8, 1/16, ect. because I already traveled those distances by traveling half way to B.This would correctly mean that we can travel an "infinite" fractional distance.Nolite Timere
 Posts: 2,649 Add as FriendChallenge to a DebateSend a Message 5/11/2014 7:16:40 PMPosted: 3 years agoAt 5/11/2014 7:14:22 PM, xXCryptoXx wrote:Well obviously the paradox isn't sound considering that travel does not work that way in reality.I can travel from point A to point B even though I must first travel the infinite number of fractions between the two points.The problem is that this is based upon your own perceptions. It is, as Zeno states, an illusion. You believe you can travel from point A to point B, but that is not the reality of the situation; thus, personal accounts are not sufficient rebuttals to the paradox.You see, if I travel half the distance between A and B I must not first travel 1/4, 1/8, 1/16, ect. because I already traveled those distances by traveling half way to B.To get to 0.5x, however, you must have first gotten to 0.25x. This is basic logic. You couldn't have simply teleported to 0.5x.This would correctly mean that we can travel an "infinite" fractional distance.Based upon our own perceptions, yes.
 Posts: 5,000 Add as FriendChallenge to a DebateSend a Message 5/11/2014 7:19:19 PMPosted: 3 years agoAt 5/11/2014 7:16:40 PM, PeacefulChaos wrote:At 5/11/2014 7:14:22 PM, xXCryptoXx wrote:Well obviously the paradox isn't sound considering that travel does not work that way in reality.I can travel from point A to point B even though I must first travel the infinite number of fractions between the two points.The problem is that this is based upon your own perceptions. It is, as Zeno states, an illusion. You believe you can travel from point A to point B, but that is not the reality of the situation; thus, personal accounts are not sufficient rebuttals to the paradox.I don't think it is an illusion on our part. I think the paradox itself is an illusion, as in that is how it would appear but it is actually false since reality would dictate that we can travel from point A to point B.You see, if I travel half the distance between A and B I must not first travel 1/4, 1/8, 1/16, ect. because I already traveled those distances by traveling half way to B.To get to 0.5x, however, you must have first gotten to 0.25x. This is basic logic. You couldn't have simply teleported to 0.5x.But by traveling to 0.5X you have already traveled all other fractional distances.This would correctly mean that we can travel an "infinite" fractional distance.Based upon our own perceptions, yes.I know there is a refutation to the paradox, and it probably involves physics but I can'tp lace my finger on it.Nolite Timere
 Posts: 2,649 Add as FriendChallenge to a DebateSend a Message 5/11/2014 7:29:31 PMPosted: 3 years agoAt 5/11/2014 7:19:19 PM, xXCryptoXx wrote:At 5/11/2014 7:16:40 PM, PeacefulChaos wrote:At 5/11/2014 7:14:22 PM, xXCryptoXx wrote:Well obviously the paradox isn't sound considering that travel does not work that way in reality.I can travel from point A to point B even though I must first travel the infinite number of fractions between the two points.The problem is that this is based upon your own perceptions. It is, as Zeno states, an illusion. You believe you can travel from point A to point B, but that is not the reality of the situation; thus, personal accounts are not sufficient rebuttals to the paradox.I don't think it is an illusion on our part. I think the paradox itself is an illusion, as in that is how it would appear but it is actually false since reality would dictate that we can travel from point A to point B.What is reality, though? Once again, you are basing reality based upon your own perspective of traveling from point A to B. "Reality" does not dictate anything. Zeno instead bases his argument off of objective facts.You see, if I travel half the distance between A and B I must not first travel 1/4, 1/8, 1/16, ect. because I already traveled those distances by traveling half way to B.To get to 0.5x, however, you must have first gotten to 0.25x. This is basic logic. You couldn't have simply teleported to 0.5x.But by traveling to 0.5X you have already traveled all other fractional distances.Except you cannot ever reach 0.5x. Or 0.25x. Or any distance at all, because any movement whatsoever would require an infinite amount of distance to cover.This would correctly mean that we can travel an "infinite" fractional distance.Based upon our own perceptions, yes.I know there is a refutation to the paradox, and it probably involves physics but I can'tp lace my finger on it.
 Posts: 25,980 Add as FriendChallenge to a DebateSend a Message 5/11/2014 7:46:52 PMPosted: 3 years agoAt 5/11/2014 12:25:58 PM, Stephen_Hawkins wrote:At 5/11/2014 11:23:25 AM, PeacefulChaos wrote:1. The infinite series of 1/2, 1/4, 1/8 ... should theoretically add up to 1, but isn't the reality that it will only get infinitesimally close to 1? So, in order for the refutation to Zeno's paradox to be valid, would we not have to accept that 0.999...= 1? Certainly, there have been arguments for this; however, I've observed multiple debates in which PotBelliedGeek manages to demonstrate that 0.999... = / = 1.http://www.debate.org...If there would be any refutations to his arguments, I'd gladly like to hear them.1) The error is just ludicrous. PBG says "1-0.9... = 0.1..." which is just flat out wrong. The elipsis clearly referred to more of the previous digit. So that means, by PBG's estimation, 1-0.999... = 0.111 ... which is false.2) He claims that 1/3 is an approximation of 0.333... which is again false. The BoP would be to show this, but ultimately we know that this is not an approximation but true. 0.333... is equal to 1/3, as we can show with simple (or bus-stop) division.3) the concept you have to "add a zero to the right" is very interesting, but just false. As it is an infinite series, you do not have an "end" to put the 0 on. A novel response, but just not true.It (being point #3) is also not true because that is simply not how you treat decimals. 10 * 0.1 =/= 0.10."Wanting Red Rhino Pill to have gender"
 Posts: 25,980 Add as FriendChallenge to a DebateSend a Message 5/11/2014 7:47:37 PMPosted: 3 years agoAt 5/11/2014 12:43:18 PM, philochristos wrote:Even if Achilles could reach the 1 distance (or x, or whatever it is), it wouldn't matter because by the time he got there, the tortoise will have moved ahead. So Achilles will never be able to catch it because every time he gets to where the tortoise was before, it will have moved ahead.Please tell me you are applying devil's advocate."Wanting Red Rhino Pill to have gender"