Stormig Posted February 26, 2004 Report Share Posted February 26, 2004 are you sure? i thought (2(inf))/(inf) = 2 Infinity divided by infinity? Quote Link to comment Share on other sites More sharing options...
Sip Posted February 26, 2004 Report Share Posted February 26, 2004 To claim that A, B and C have the same number of points implies that we know how many points each have. Not necessarily. So here's how the proof goes ... in order to show that both have the same number of points, all we need to come up with is a 1 to 1 mapping from any point you pick on one line to a unique point on the other line. To do this, we have: Line 1: __________________ / a / Line 2: __/______ / b / `p I will pick a reference point p. For any point 'a' you pick on line 1, I will just draw the line connecting a to p. This will result a unique point b on line 2. Note that the order in which we pick points from the line (either from the shorter one or from the longer one) is arbitrary so this does in fact create a 1 to 1 mapping between any point on line x to any point on line y and vice versa. The proof relies on some fundamental postulates but otherwise, it shows how both those lines have the same number of points! Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 Infinity divided by infinity? You are right, I am surprised that Harut presented that, as it is one of the 7 undeterminated forms in mathematic, first you have to wave off the undetermination by the notion of limits... But I do understand still Harut point, it could be seen as this. lim (2x/x) x -> inf The answer to that will be 2. But what Sip present is a different cases of infinity, and it is even debated among some mathematicians, I decided to not reveal the name of the mathematician as people will understand the whole point after a google search. Edward and Sasun, the "Proof" is rather graphical, it can be translated by a demonstration form, but the beauty of it is very graphical. Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 You are right, I am surprised that Harut presented that, as it is one of the 7 undeterminated forms in mathematic, first you have to wave off the undetermination by the notion of limits... But I do understand still Harut point, it could be seen as this. lim (2x/x) x -> inf The answer to that will be 2. But what Sip present is a different cases of infinity, and it is even debated among some mathematicians, I decided to not reveal the name of the mathematician as people will understand the whole point after a google search. Edward and Sasun, the "Proof" is rather graphical, it can be translated by a demonstration form, but the beauty of it is very graphical. Too late, Sip answered. Quote Link to comment Share on other sites More sharing options...
Sip Posted February 26, 2004 Report Share Posted February 26, 2004 Too late, Sip answered. You still didn't say who came up with it. Unless you want to take credit for it! Edit: Nevermind, just read your post. Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 You still didn't say who came up with it. Unless you want to take credit for it! Hmmmm.... No fair.... no fair... Saying it that way... It was Cantor, one of my favoured. Not because he was mad and kind of schizophrenic. Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 Cool illustration Sip, I like the graphical proof, now I remembered something like that I have know. It is in fact equivalent to my "stretching" argument above. But still there is something missing. How do you explain the difference C? Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 Cool illustration Sip, I like the graphical proof, now I remembered something like that I have know. It is in fact equivalent to my "stretching" argument above. But still there is something missing. How do you explain the difference C? In fact, there is something missing in his demonstration... but now that you have the name of the mathematician, just use google and voila. Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 In fact, there is something missing in his demonstration... but now that you have the name of the mathematician, just use google and voila. What? that the point p is not arbitrary, and how to find that point? Quote Link to comment Share on other sites More sharing options...
gevo27 Posted February 26, 2004 Author Report Share Posted February 26, 2004 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 Thats not the case here. That definition is most likely used to explain the notion of infiniti to high school kids at most. I am saying if infiniti was considered the number N, then it is not infiniti, it is finite.. lol.. Because now N represents a "number" no matter how large it is, so thats why we call it infiniti, and it is neither a "variable" nor a number.. it is the "concept" of a value or N getting very very very large, how large? very very very very very large, then it keeps going.. LMAO.. ofcourse thats obviouse, but remember, do not refer to infiniti as a number, and you cannot try to proov anything with infiniti by incorporating it into various mathematical equations, formulas etc..... you cannot call infiniti=N then say, 3N/N = N, no, but you can do what Domino did, take the limit, or differentiate... Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 What? that the point p is not arbitrary, and how to find that point? No, thats not what is missing... what is missing is more like clarity... I was expecting him to draw all the lines... I will be trying to find one... Here, you will understand why Cantor is one of my favoured. http://www.asa3.org/ASA/PSCF/1993/PSCF3-93Hedman.html Pay more attention to the part regarding the universe and undeterminism. Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 Thats not the case here. That definition is most likely used to explain the notion of infiniti to high school kids at most. Gevo, that's the definition in math (to my knowledge), it doesn't matter high school or no. What is the definition that you know? I am saying if infiniti was considered the number N, then it is not infiniti, it is finite.. "N" is just a notation, we are defining something, we are not saying it is finite. you cannot call infiniti=N then say, 3N/N = N, no, but you can do what Domino did, take the limit, or differentiate... Before you take the limit you need a definition of infinity. And what I gave is the definition. Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 No, thats not what is missing... what is missing is more like clarity... I was expecting him to draw all the lines... I will be trying to find one... OK, I will not search on Google, you do the job and let us know Here, you will understand why Cantor is one of my favoured. http://www.asa3.org/ASA/PSCF/1993/PSCF3-93Hedman.html Pay more attention to the part regarding the universe and undeterminism. I am surprised you put this link I will try to read it. Quote Link to comment Share on other sites More sharing options...
Sip Posted February 26, 2004 Report Share Posted February 26, 2004 Guys I have a big ass deadline at 5pm and you are really tempting me here to not work! Shame on ALL of you Quote Link to comment Share on other sites More sharing options...
gevo27 Posted February 26, 2004 Author Report Share Posted February 26, 2004 Gevo, that's the definition in math (to my knowledge), it doesn't matter high school or no. What is the definition that you know? "N" is just a notation, we are defining something, we are not saying it is finite. Before you take the limit you need a definition of infinity. And what I gave is the definition. If n was only a notation, then i understand, other than that it cannot represent the "number" infiniti... dangit,, LOl.. iv said ahundred times infiniti is not a number, if it were, we could add 1 to it and get, infiniti plus 1.... but that makes no sense... Ok, sasun, explain to me what the answer to 5*Infiniti is= and that proof with the lines and stuff, yeah kinda weird way to thin k about it, but i understand the point it is trying to mek, whcih is correct ofcourse, cause we have no idea ourselves what infiniti is.. lLMAO... to us it goes on forever, but what is forever, and can we eve ask the question, how long would a line be if it went on forever?? hahah... what does it mean for us to be infinitly close to a number N, if we take the limi, then we understand, but if we dont ask fo the limit, then we are stuck, no way to explain how close we really are to N.... or is there sasun??? Quote Link to comment Share on other sites More sharing options...
Anileve Posted February 26, 2004 Report Share Posted February 26, 2004 As Azat would say.... Geeks Quote Link to comment Share on other sites More sharing options...
gevo27 Posted February 26, 2004 Author Report Share Posted February 26, 2004 As Azat would say.... Geeks i dont know anileve jan, i did score a 60% on his geek test.. thats failing though.. LMAO... im not a geek, i just tend to ponder about seemingly geekish stuff.. HAHAHA Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 If n was only a notation, then i understand, other than that it cannot represent the "number" infiniti... dangit,, LOl.. iv said ahundred times infiniti is not a number, if it were, we could add 1 to it and get, infiniti plus 1.... but that makes no sense... Ok, sasun, explain to me what the answer to 5*Infiniti is= and that proof with the lines and stuff, yeah kinda weird way to thin k about it, but i understand the point it is trying to mek, whcih is correct ofcourse, cause we have no idea ourselves what infiniti is.. lLMAO... to us it goes on forever, but what is forever, and can we eve ask the question, how long would a line be if it went on forever?? hahah... what does it mean for us to be infinitly close to a number N, if we take the limi, then we understand, but if we dont ask fo the limit, then we are stuck, no way to explain how close we really are to N.... or is there sasun??? Eh Gevo, I am not sure what you want me to answer. I think we all agree that we cannot have a good understanding of the "infinity" concept. Tell me what "infinity" is and I will tell you what 5*infinity equals Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 26, 2004 Report Share Posted February 26, 2004 OK, I will not search on Google, you do the job and let us know I am surprised you put this link I will try to read it. Sorry Sasun for the late anwer, I am preparing something right now and have no much time, maybe tonight... As for the link... I have chosen that one, because it was the only way to make you read about him, I thought hat the word "Christian" will influence you in your decision to read... Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 That's OK Domino, you can post when you have a chance. And good thinking on choosing the article Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 26, 2004 Report Share Posted February 26, 2004 Azat, when you saw us talking about infinity, I wonder if you thought about that Infinity car you had among your choices, and thought something like this "Hahahaha... look at those geeks and me, I am thinking of getting this shiny Infinity and driving to ladies to sweet-talk, and what the hell are those geeks thinking about! " Quote Link to comment Share on other sites More sharing options...
Harut Posted February 27, 2004 Report Share Posted February 27, 2004 You are right, I am surprised that Harut presented that, as it is one of the 7 undeterminated forms in mathematic, first you have to wave off the undetermination by the notion of limits... But I do understand still Harut point, it could be seen as this. lim (2x/x) x -> inf The answer to that will be 2. duh. sorry. Quote Link to comment Share on other sites More sharing options...
DominO123 Posted February 28, 2004 Report Share Posted February 28, 2004 (edited) Sorry for my late answer Sasun, it is difficult to find exactly what I wanted from the web, so I will be posting some stuff regarding this until I draw and submit you the visual demonstration... I will be posting you the idea behind the "lines" demonstration of two set of "defined" infinit. http://home.ican.net/~arandall/abelard/math12/Cantor.html Here a short indication of the "problem" with Cantors defined(as opposed to non-defined) infinit. http://acad.udallas.edu:8080/~wojtowic/Sem/Josh.pdf And here, a little more compleat description of the actual real problem. http://www.com2com.ru/alexzen/papers/Canto..._of_Cantor.html Cantors notion is mind buggling... as it tries to define infinit... if two lines with different size have the same number of "points" or you you prefer "numbers" that would mean that the two infinits are equal, you are defining infinits, determinating them, while usually they are not... the presentation of Cantors sets of "numbers" and his axioms gave birth to the Cantors Paradox, and this was one of the reasons of it. But I do like his notion pretty much, as I do believe his demonstration as true and as well believe that some of the mathematicians that tries to sell that Cantors "Proof" and diagonal "proof" contain a mistake don't recognise Cantor notion as it should, that means a paradox. This of course exist, when the size of the lines are determinated, this is why I said to Sip that if you have two set of lines that are not determinated, it does not work anymore, even if using Cantors demonstrations we can manipulate and make it work, but logically it should not... again we arrive to a paradox. I will maybe write more about this thing later, as there is one thing brought by Cantor that always facinated me... that support my multiple-universe notion. Edited February 28, 2004 by Fadix Quote Link to comment Share on other sites More sharing options...
Sasun Posted February 29, 2004 Report Share Posted February 29, 2004 Domino, thanks for the links! I have been reading and thinking (and getting nostalgic) I am still digesting parts of the links (I have only read parts) - it is not that easy to understand all these materials. Please do draw and post the visual demonstration of Cantor's proof. I thought that it was clear already but maybe not. All I can see is a paradox, a contradiction. I showed above the contradiction unless I was wrong and am not aware of it. I have thought of another way to show the contradiction, I am still working on it. I tried to understand Cantor's Paradox but I am not quite sure what it means. I know very little of set theory. http://mathworld.wolfram.com/CantorsParadox.html http://planetmath.org/encyclopedia/CantorsParadox.html Can you tell me in human words what part is paradoxical? Perhaps in that case I will understand why you mentioned it. Quote Link to comment Share on other sites More sharing options...
Sip Posted February 29, 2004 Report Share Posted February 29, 2004 ... 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? Yes ... that is not "indeterminate" as Domino would call it. Inf + Inf = Inf. So that is not a contradiction. Using the proof above, you can show N(A)=N(B), and N(A)=N(C) and N(C)=N(B) and N(A)=N(B)=N(C)=infinity Quote Link to comment Share on other sites More sharing options...
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