This is one of those times I really hate the timedifference between Europe and America, while you guys are discussing this stuff almost in real time I always have to wait till the next morning to see how things developped. Anyway Truestory, tell me honestly, would you have attacked my statement about infinity as violently if I hadn't included god in the picture ? I think your attack was more based on emotions then on pure mathematics, your anger against Boris and FyreStar who came to my defence (who I here by thank) somehow confirms this. Now if we could leave god and emotions out of the picture and simply look at the notions themselves. First we must agree that mathematics is all about logical consistent statements that form a framework. The reason why a/infinity = 0 is to have a consistent mathematics. Lets look at multiplication itself : if I say that a * b = c (with a, b and c natural numbers for simplicity) then this means that a + a + a + ... + a = c if you count the a's in the sum there should be b of them. Or one can say b + b + b + ... + b = c now there should be a b's, this property is called cummutativity. Thus we have the relation : a * 0 = 0. Any finite number multiplied by 0 equals zero. Why ? because we sum 0 a's on the left side or we have 0 + 0 + 0 + ... + 0 = 0 so we sum a 0's. 0, being the neutral element of the summation (this means 0 + a = a + 0 = a) makes this a valid statement. On the other hand we have : a * inf = inf this is quite obvious but look at the two statements, they are both of the form : a * something = something, for the multiplication this something can only be 0 of infinity ! All other solutions are incorrect. Lets look at the inverse of 0 and infinity, the inverse X in multiplication of a number A means that X * A = A * X = 1. So X = 1/A. If we look at the inverse of 0 then we must have a number X for which 0 * X = 1. But we have seen that the product of any finite number multiplied by 0 must equal 0 this means that X is not a finite number or in other words <FONT SIZE=5 COLOR="#ff0000"> X is infinite </FONT> !! I hope this convinces you. ------------------ "If I have been able to see further, it was only because I stood on the shoulders of giants." Isaac Newton
No, Plato. This does not convince me. As you know, in reality, zero can never be the denominator. Oh, yes, we can put it on paper, but it will be a FALSE statement. Try it on your calculator with any number. You will be notified that you have made an ERROR. No biggy. PS Our mutual perceptions of violence and anger are on two different ends of the spectrum! Perhaps you perceive the strength of my arguments as violent and/or angry? ------------------ Have a great day! [This message has been edited by truestory (edited September 21, 1999).]
Plato, What? You still didn't disprove that those concepts are unseen eternal things. The concepts are REPRESENTED on paper or on a calculator or on a computer screen, but the concepts themselves (which rule the physical universe) are unseen and eternal, which the bible states; just like I said before. Why is it so hard to understand? It's basically very simple. There is an intelligence behind all of this. Love to all, Dorkus ka Dabra ------------------ "What is your favorite color?" "Blue...No, Yellow! AAAAAAaaaaaahhh!" Monty Python
truestory, And if you write a computer program (say, in C) to divide a number by 0 and print out the result -- if you are careful to shut down the division-by-0 interrupt you most likely will get this answer: "INF" -- meaning infinity. Most calculators were designed for use by ordinary people, not professional mathematicians; their behavior does not a point make. And why don't you stop proclaiming things about which you have no idea? Go study mathematics, as it truly is in full glory of reality. ------------------ I am; therefore I think. [This message has been edited by Boris (edited September 23, 1999).]
Dork, And just as the concepts are represented on paper when you write them down -- so are they represented in you brain when you discover or memorize them. Beyond your brain, they do not exist. And they are not eternal, absolutely true, unshakable and fundamental -- your entire knowledge, whether you like it or not, is composed of theories -- which, not unlike scientific theories, <u>can be</u>, and sometimes <u>are</u>, disproven. Get...it...yet...? ------------------ I am; therefore I think.
>And just as the concepts are represented on paper when you write them down -- so are they represented in you brain when you discover or memorize them. Beyond your brain, they do not exist. And they are not eternal, absolutely true, unshakable and fundamental -- your entire knowledge, whether you like it or not, is composed of theories -- which, not unlike scientific theories, can be, and sometimes are, disproven. Get...it...yet...?< Yes, Boris, I..do...get...it...yet. Beyond your brain they do not exist? Yes they DO!! How many times do I have to explain it? If I die and what you say is true, then nothing matters.....to me, but to you they still do since you're alive (let's assume for this example). If you die and there's no God, then nothing matters anymore.....to you; but to me it still does. That's the entire arguement. I can see your point of view but you obviously cannot see mine. There OBVIOUSLY is something called existence outside of what we can experience or think of in our brains because if the opposite were true, then nothing I myself experience is real, therefore you are not real, my mom and dad (which I'm not experiencing in this moment) does not exist, the Statue of Liberty does not exist, the New York Stock Exchange does not exist, the national capitol does not exist, Bill Gates does not exist, antelope in Africa do not exist, the metal used in cars that is found in the ground does not exist, the telephone company making this communication possible does not exist. OBVIOUSLY IT DOES!!!!!!!!!!!!!! DO...YOU...GET...IT...YET? :\ [This message has been edited by Dork (edited September 23, 1999).]
Dear Boris, I am sorry that you are having another bad day (your arrogance and nastiness are showing again!) I'll say another prayer. As Blacktubby could rewrite the definition of certain words to suit his purpose, so could you rewrite the laws of mathematics to suit yours. However, I do not find that as being the professional thing to do. [This message has been edited by truestory (edited September 23, 1999).]
truestory, I meant what I said about studying mathematics. It is just infuriating when someone starts making authoritative statements about a subject they do not know well enough. It's like if I started to proclaim that nowhere in the Bible does it say anything about a huge Ark -- without having ever done even a little research on the subject. And if you objected, I would call you mean, arrogant and close-minded. Perhaps now, given the analogy, you could see why your remarks annoy me so? I understand that you may have had algebra and geometry in school -- but probably not calculus. It is calculus (or perhaps pre-calculus) where you discuss infinities and limits for the first time. And you can take my and Plato's words for what we say; we know what we are talking about. If you doubt it, find any professional mathematician and confirm it. <hr> As for the "get it yet", Dork did it first. Go blame him; he started it. Please Register or Log in to view the hidden image! ------------------ I am; therefore I think. [This message has been edited by Boris (edited September 23, 1999).]
Dork, Of course there is such a thing as reality outside of the mind. What does not exist, is a single human concept that is an eternal or absolute truth. In case you haven't noticed it, that's been my big and overriding thesis here, and the very reason I keep debating you. ------------------ I am; therefore I think.
Boris, First - For a self-proclaimed scientist, you certainly are exhibiting a pattern of making assumptions and drawing conclusions about me without first getting your facts straight. Second - I find it intriguing that you took great exception to my suggestion about trying my assertion on a calulator (to the point of causing yet another one of your failed ATTEMPTS at belittling me). Yet, you seemed to have no problem with the very same suggestion that your friend Plato made in his original erroneous mathematical example. Third - I do not know or proclaim to know your level of education or the extent of your knowledge (or lack there of). It is also quite apparent that you know nothing about mine. Without getting into a war of credentials, let me assure you that mine goes way beyond calculus. [This message has been edited by truestory (edited September 23, 1999).]
truestory, Ok, if you want to take it down to character assassination, here we go. That was a quote from you. Now, I would kindly ask you to quote from Plato where "he says the same thing". As for "credentials" -- I do not assume that you don't know calculus, I <u>know</u> it, by simply reading your posts. If you suggest that you actually have had exposure to higher math, then I must conclude that you slept through most of it. ------------------ I am; therefore I think.
truestory, If your knowledge of mathematics is so great could you perhaps elaborate a bit on the following simple problem : Does the integral with bounderies +infinity and +R (with R being a positive real number) of dx/x^2 has a finite answer ? If so what is the answer ? Do you recognise the formula ? If so what did you just calculate ? ------------------ "If I have been able to see further, it was only because I stood on the shoulders of giants." Isaac Newton
Hello Boris, First of all - I did not say that "he (Plato) says the same thing". Please get your facts straight! What I indicated was that we both made the same suggestion about trying our assertions on a "calculator". Here is Plato's suggestion: "This is a simple mathematical truth that you can verify on your calculator by dividing a number by an increasingly large number, the result will become smaller and smaller, in the limit to infinity it will become zero !" Yes, the great mathematician Plato used the ORDINARY "calculator" word. Shame on Plato! (Your bias is obvious, Boris. The way you tried to use the use of a calculator, of all things, to try and imply that you and Plato were above me some how, was utterly ridiculous!). Now, if you cannot acknowledge this, then I am not going to bother discussing anything else with you. Second of all - Your "character assassination" remark smells like the old "I can dish it out, but I can't take it" routine. I have no need to assassinate your character. As far as I'm concerned, it's been committing suicide. [This message has been edited by truestory (edited September 24, 1999).]
Truestory, could you please answer my questions ? Besides, I have an other one for you : Is it possible to take the squareroot of a negative number ? Try it first on your calculator perhaps... ------------------ "If I have been able to see further, it was only because I stood on the shoulders of giants." Isaac Newton [This message has been edited by Plato (edited September 24, 1999).]
Plato, Before I go any further in my discussions with you, I need to know what your character is like so please answer this: Was Boris' proposed C-programming solution a mathematical truth, or was it a way to debug the inherent "Division by Zero" problem to avoid a run-time error and to be able to have more control over an application?
They said it couldn't be done, Plato... but you and Boris have proved it... you are the roots of negativity... squared!
truestory : Boris C-program example was there to show how programmers omitted the 'division by zero' problem in C. The reason though why they have this problem in the first place is because computers (and calculators) have finite memories, meaning they can't represent infinitly large numbers. This limitation does nothing away from the fact that 1/0 = infinity as being a mathematical truth. I find this a strange way to deduce my character from though, what have you learned from my answer ? ------------------ "If I have been able to see further, it was only because I stood on the shoulders of giants." Isaac Newton
Something else truestory, perhaps you know this all ready but zero was one of the last numbers to be discovered. It was invented during the early middle ages in India and was passed to Europe via the Arabians. Zero is not like any other number you see, if you include it with the other real numbers, the product function loses it's group property ! One could even debate if zero is a proper reeel finite number because it behaves very differently then all the other numbers. The reason lies in it's close relation with infinity : zero is the infinitly small number, take any small number, zero is smaller ! You see how very different the world of the infinities is from our finite world ? ------------------ "If I have been able to see further, it was only because I stood on the shoulders of giants." Isaac Newton
Plato states: "This limitation does nothing away from the fact that 1/0 = infinity as being a mathematical truth." What I have further deduced about your character from your statemement above is this... either: 1) You are not the mathematician that you purport yourself to be, or 2) That you have a character flaw which causes you to distort the facts (the truth about the mathematical axiom with respect to 1/0) to suit your own purpose. Why/how do I deduce this? Well, for starters, as any knowledgeable mathematician can tell you, the mathematical axiom (the truth, the fact) with respect to 1/0 is that 1/0 is "undefined." The answer is... there is no answer. That is why mathematicians refer to numbers that are divided by zero as "undefined." Some people tend to think of them as being infinite, but this isn't exactly true (in other words, it is not a mathematical fact, Plato). The fact is, there simply is no answer. The field of axioms lay down a set of rules about how to put numbers together to get other numbers. Division by zero contradicts these rules (this proof is usually taught in beginning algebra classes). Technically speaking, division by zero is not necessarily impossible. Rather, division by zero is provably contradictory to a given set of mathematical rules and therefore is not permitted. One can "interpret" 1/0 as positive or negative infinity (Which one is it? Positive or negative infinity? Instead of just assigning one willy-nilly, in mathematics, we say that infinity isn't a number, and that 1/0 is "undefined"). If one does interpret 1/0 as positive or negative infinity, they should be prepared to deal with whatever happens. Some people say that 1/0 is infinity as a kind of short-hand for "interpreting" what happens to 1/X as X approaches zero. This is done as a convenience. As you probably know, 1/0=infinity is NOT a mathematical truth and I think this forum would be better served if you would refrain from stating that it is. The FACT is this: The mathematical truth about 1/0 is that it is "undefined."
truestory, First of all, I cannot believe you decided that I went after you simply because you mentioned claculators. As far as I recall, you utilized the example of a calculator to "demonstrate" that division by zero is an "ERROR", not mathematically allowable. To counter your point, I pointed out another example of a calculator, which actually treats division by zero as a legal operation resulting in infinity. The point was that calculators were designed for general use and convenience, and the designers don't want to confuse the mathematical non-cognoscenti with such "advanced" concepts as limit behavior or imaginary numbers (as is the case with Plato's second example.) Secondly, for positive real numbers x and n, as n->0, lim(x/n) = +inf. Similarly, lim(-x/n) = -inf. Positive and negative infinities do indeed exist. They are even routinely used in integrals of certain functions, such as the Gaussian. Even in algebra, you have a precise definition of such a thing as "infinite slope" -- the slope of a vertical line (and that infinity, incidentally, arises precisely because of division by 0, though in the case of lines the infinite slope can be either positive or negative, depending on the way you measure it. Although, if the line is a time-parametrized curve that approaches vertical from a finite slope at time 0, then its slope in the limit still has a well-defined sign.) The irrational numbers such as 2^(0.5), pi, e -- cannot be defined by a finite formula. They invariably arise either from limit expressions, or from infinite series. For example, one of the ways to define the natural number is: e = lim[(1+n)^(1/n)], n->0. An alternative, and totally equivalent, definition is lim[(1+1/x)^x], x->inf. As you can see, mathematically, 1/0 and inf are interchangeable. In fact, the irrational numbers have <u>infinitely</u> many digits after the decimal point, which is also a fact that is actually <u>proven</u> mathematically. As I said earlier, in Algebra they tell you that division by 0 is not allowed, and the result is undefined. They also tell you that an even-power root of a negative number is not allowed, and the result is undefined. In both cases, they blatantly lie to you. The reason they lie, is because they want you to take it one step at a time; it would be too much to jump to calculus before you learned algebra, or to talk about infinities or non-Real numbers before you got comfortable with the number line. The point is, truestory, you are simply wrong. Swallow the fact and move on. Perhaps it would serve you better to spend the time browsing through an introductory text to higher mathematics -- rather than trying to argue such a hopelessly doomed case from such a limited perspective. ------------------ I am; therefore I think. [This message has been edited by Boris (edited September 24, 1999).]
