gevo27 Posted February 26, 2004 Author Report Share Posted February 26, 2004 Here is the mathematical definition of a point from mathworld: So given this definition, each of those lines I drew above has an infinite number of points on it. But how can one be longer than the other if both have an infinite number of points? That is the question I am posing. So after you see the answer, the concept of infinity will become more clear. And Sasun, here is an example where you can see infinity right there in front of you! ok, i just saw this,, lol.. i didnt read all of it before i posted last.. but i knew what you were getting at And sasus, you are right, which is actually my underlying point, we cannot determin such things because of our own concpetion, or lack of, infiniti... but.. its kinda crazy to start asking for definitions of infiniti which we can fully perceive.. LMAO.. i can see why mathematicians would commit suicide over this notion hahahah Domino, i dont se eyou point where the closest number to 5 given 5cannot equal 5 is 5... need clarification if you expect me to understnad 5 doesnt eqaul 5 but it equals 5. LMAO.. Quote Link to comment Share on other sites More sharing options...
gevo27 Posted February 26, 2004 Author Report Share Posted February 26, 2004 PEOPLE, PEOPLE, PEOPLE!!!!!!!! http://www.thegev.com/images/potd/letsnotjumptoconclusions.jpg why not, she would conclude her theory before us// HAHAHA LMAO Quote Link to comment Share on other sites More sharing options...
Sip Posted February 26, 2004 Report Share Posted February 26, 2004 is that good enough ? It is in fact true that both lines have the same number of points. It can be shown very easily. They both have an infinite number of points. The longer line has exactly the same number of points as the smaller line. Of course such a grand statement is useless without a proof. So how would you prove it? Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 Domino, i dont se eyou point where the closest number to 5 given 5cannot equal 5 is 5... need clarification if you expect me to understnad 5 doesnt eqaul 5 but it equals 5. LMAO.. gevo, it is a prolongation of the R - N = R. OK I know, we can make numbers say what we want. BTW Sip, you are cheating a little don't you believe so? As the infinit notion you are presenting is the infinitly small, while in the cases of the infinitly big, those "equalities" don't exist between different infinits. Quote Link to comment Share on other sites More sharing options...
Sip Posted February 26, 2004 Report Share Posted February 26, 2004 Fad, that is exactly the point I am trying to make! Think of the largest number you can imagine ... call it alpha. Think of 5 and the number closest to 5, not equal to 5. Call it 5 + delta. I am trying to say that between 5 and 5+delta there are just as many numbers as between - alpha and + alpha. And I can prove it for arbitrary alpha and delta. [Edit]: I am assuming (postulating) that a number corresponds to a point on a line (the number is the coordinate of the point in 1-dimension). Quote Link to comment Share on other sites More sharing options...
gevo27 Posted February 26, 2004 Author Report Share Posted February 26, 2004 It is in fact true that both lines have the same number of points. It can be shown very easily. They both have an infinite number of points. The longer line has exactly the same number of points as the smaller line. Of course such a grand statement is useless without a proof. So how would you prove it? you cant proove it thats the problem LMAO.. but the number of points on one line is not equal to the number of points on the other line, because there is no number for either line .. Thus you would have to say your satement this way// "the concept of points on one line is equal to the concept of points on the other line" then i can answer yes, that is true... lol.. and Domino jan, i have yet to figure ou that formula, and ofcourse,, number can be manipulated very easily infact its one of the reason why so many computations are possible in both physics and mathematics! especially calculas and differentiables Quote Link to comment Share on other sites More sharing options...
Sip Posted February 26, 2004 Report Share Posted February 26, 2004 Actually the proof is quite elegant so I am hesitant to give it away too quickly Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 Fad, that is exactly the point I am trying to make! Think of the largest number you can imagine ... call it alpha. Think of 5 and the number closest to 5, not equal to 5. Call it 5 + delta. I am trying to say that between 5 and 5+delta there are just as many numbers as between - alpha and + alpha. And I can prove it for arbitrary alpha and delta. [Edit]: I am assuming (postulating) that a number corresponds to a point on a line (the number is the coordinate of the point in 1-dimension). Sip, why just not call them Epsilun. Well, the point I was trying to make Sip is that those lines equalities works when the distance of the line is finit, it stops to be true when its distance is not determinated(infinit). This is what I mean when I say infinitly small, what you bring explains the inifinitly small, that says nothing about the infinitly big. Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 "the concept of points on one line is equal to the concept of points on the other line" then i can answer yes, that is true... lol.. and Domino jan, i have yet to figure ou that formula, and ofcourse,, number can be manipulated very easily infact its one of the reason why so many computations are possible in both physics and mathematics! especially calculas and differentiables Hey! Hold on kid, numbers can be manipulated, we can make say numbers everything, but you can not compare physical problems with mathematical ones... there is really proves in math, those euqlities are fundamental, they are pure, nothing to be compared with physic here... from those equalities you can make say everything what you want.... but those equalities are pure and perfect. Sip, if you think I will let you present the proof and take the credit for it... in your dreams... I prefer giving clues to him... Gevo Jan, take a pen draw those two lines, and try to divide them in a way, where you can link them with lines and end up that theoritically you could link each "theoritical" "points" with each others... if you have problems and want more clues, feel free to ask, as there is no question that Sip will take the credit for such a genius "proof." Quote Link to comment Share on other sites More sharing options...
Sip Posted February 26, 2004 Report Share Posted February 26, 2004 I won't take credit for the proof. My advisor showed it to me one day a few years ago while we were working on an unrelated problem. I don't know where he saw it but I am sure it is probably a well known thing ... if we had a mathematician among us, I'm sure he would tell us. Oh where oh where is MJ. Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 I won't take credit for the proof. My advisor showed it to me one day a few years ago while we were working on an unrelated problem. I don't know where he saw it but I am sure it is probably a well known thing ... if we had a mathematician among us, I'm sure he would tell us. Oh where oh where is MJ. Sip, don't tell me you don't know who was the mathematician that came up with this proof? Quote Link to comment Share on other sites More sharing options...
Sip Posted February 26, 2004 Report Share Posted February 26, 2004 I have no idea ... math is not my strongest subject. Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 I have no idea ... math is not my strongest subject. Hmmm... lemmee see the prize it will cost you for me to tell it. Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 Actually I am not quite sure that those two lines have exactly the same number of points. Let's say line A is the longer line, and line B is the shorter one. Let's say A has N(A) number of points, and B has N(B ) number of points. Let's assume that as Sip and Domino claim N(A)=N(B ). A ________________________________________ B ______________________________ C __________ There is a third line, C which is the difference of A and B. Lenght(A)-length(B )=lenght©. Now, according to the same assumption, C has the same number of points as A, N(C )=N(A). Under normal assumptions lenght and number of points would be proportional - the more point you add to the line, the longer it is. So it follows that since length(B )+length(C )=length(A) then N(B )+N(C )=N(A). Since we assumed that N(B )=N(A) and N(C )=N(A), then we can substitute in the former equation and get N(A)+N(A)=N(A). Now, this is not true with finite numbers. Could this be true with infinite numbers? I would say that the answer is either no or undetermined. For all practical purposes the answer is yes. BUT... Quote Link to comment Share on other sites More sharing options...
gevo27 Posted February 26, 2004 Author Report Share Posted February 26, 2004 Hey! Hold on kid, numbers can be manipulated, we can make say numbers everything, but you can not compare physical problems with mathematical ones... there is really proves in math, those euqlities are fundamental, they are pure, nothing to be compared with physic here... from those equalities you can make say everything what you want.... but those equalities are pure and perfect. Sip, if you think I will let you present the proof and take the credit for it... in your dreams... I prefer giving clues to him... Gevo Jan, take a pen draw those two lines, and try to divide them in a way, where you can link them with lines and end up that theoritically you could link each "theoritical" "points" with each others... if you have problems and want more clues, feel free to ask, as there is no question that Sip will take the credit for such a genius "proof." FFadix you cant manipulat infiniti, which is the "concept" not even a number.. of this discussion,, ihave seen irrational profes that have literll proved 1+1=3... so.. numbers shnumbers.. LMAO.. im talking about a concept we dont even understand, we just gave it a name.. Quote Link to comment Share on other sites More sharing options...
Azat Posted February 26, 2004 Report Share Posted February 26, 2004 You nerds continue to talk about your nerdy stuff, while I go and sweet talk to all the ladies. Quote Link to comment Share on other sites More sharing options...
ED Posted February 26, 2004 Report Share Posted February 26, 2004 Actually I am not quite sure that those two lines have exactly the same number of points. Let's say line A is the longer line, and line B is the shorter one. Let's say A has N(A) number of points, and B has N(B ) number of points. Let's assume that as Sip and Domino claim N(A)=N(B ). A ________________________________________ B ______________________________ C __________ There is a third line, C which is the difference of A and B. Lenght(A)-length(B )=lenght©. Now, according to the same assumption, C has the same number of points as A, N(C )=N(A). Under normal assumptions lenght and number of points would be proportional - the more point you add to the line, the longer it is. So it follows that since length(B )+length(C )=length(A) then N(B )+N(C )=N(A). Since we assumed that N(B )=N(A) and N(C )=N(A), then we can substitute in the former equation and get N(A)+N(A)=N(A). Now, this is not true with finite numbers. Could this be true with infinite numbers? I would say that the answer is either no or undetermined. For all practical purposes the answer is yes. BUT... Sasun jan those lines have exacly 2 endpoints, this is 15 years of CAD talking, in our business and in drawings in general if its a line where it begins and ends paralel then can't have more then 2 points/endpoints. Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 Sasun jan those lines have exacly 2 endpoints, this is 15 years of CAD talking, in our business and in drawings in general if its a line where it begins and ends paralel then can't have more then 2 points/endpoints. Edo jan, what about the other points between the 2 endpoints Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 You nerds continue to talk about your nerdy stuff, while I go and sweet talk to all the ladies. Hahahaha, Azat we do all the hard work, and you do the sweet talk? That's not fair. I think you should prove a theorem or two before you go to ladies I think ladies will agree with me on this Quote Link to comment Share on other sites More sharing options...
ED Posted February 26, 2004 Report Share Posted February 26, 2004 (edited) ok you got me you can say each one has a midpoint as well, Edited February 26, 2004 by Edward Quote Link to comment Share on other sites More sharing options...
ExtraHye Posted February 26, 2004 Report Share Posted February 26, 2004 Hahahaha, Azat we do all the hard work, and you do the sweet talk? That's not fair. I think you should prove a theorem or two before you go to ladies I think ladies will agree with me on this Nope, we like Azat just the way he is. Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 Nope, we like Azat just the way he is. But but... have you ever considered the same Azat the way he is, plus he can prove a theorem Quote Link to comment Share on other sites More sharing options...
gevo27 Posted February 26, 2004 Author Report Share Posted February 26, 2004 Actually I am not quite sure that those two lines have exactly the same number of points. Let's say line A is the longer line, and line B is the shorter one. Let's say A has N(A) number of points, and B has N(B ) number of points. Let's assume that as Sip and Domino claim N(A)=N(B ). A ________________________________________ B ______________________________ C __________ There is a third line, C which is the difference of A and B. Lenght(A)-length(B )=lenght©. Now, according to the same assumption, C has the same number of points as A, N(C )=N(A). Under normal assumptions lenght and number of points would be proportional - the more point you add to the line, the longer it is. So it follows that since length(B )+length(C )=length(A) then N(B )+N(C )=N(A). Since we assumed that N(B )=N(A) and N(C )=N(A), then we can substitute in the former equation and get N(A)+N(A)=N(A). Now, this is not true with finite numbers. Could this be true with infinite numbers? I would say that the answer is either no or undetermined. For all practical purposes the answer is yes. BUT... sasun jan, there are only finite numbers, there is no such thing as "infinit" numbers.. We cant think of infiniti as a number, you cannot compute infitie plus infiniti... thats why it is abstrract, and that is the same case i am trying to mek.. lol.. and yes, line A B C all have the same amount of points Quote Link to comment Share on other sites More sharing options...
Harut Posted February 26, 2004 Report Share Posted February 26, 2004 It is in fact true that both lines have the same number of points. are you sure? i thought (2(inf))/(inf) = 2 Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 sasun jan, there are only finite numbers, there is no such thing as "infinit" numbers.. We cant think of infiniti as a number, you cannot compute infitie plus infiniti... thats why it is abstrract, and that is the same case i am trying to mek.. lol.. and yes, line A B C all have the same amount of points In mathematics, infinity is defined like this: number N is said to be infinitely large if no matter what number x we choose N>x always holds true. Now, you make up your mind to see if there is such a thing as infinite number or not To claim that A, B and C have the same number of points implies that we know how many points each have. All we know is that each has an unknown number of points. We cannot compare unknown numbers. The only certainty is that no matter how large a number we think of, the number of points on each of the lines (A, B and C) is larger than that number. However, 2 arguments. One could argue that in order to get from B to A we do have to add more points. One could also argue that in order to get from B to A we do not need to add points but only "stretch" B without adding more points. Quote Link to comment Share on other sites More sharing options...
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