john_gabriel

Indeed it is standard calculus. You do not understand and that's where the flaw lies. You need to understand very quickly but I somehow doubt you have the mental ability? Of course when there are those like you running the show, you can do whatever whimsical things you please... Cap'n Refsmmat , John Cuthber - both these individuals voted that they don't get it! Too funny. Why am I not surprised... You evidently did not understand the first post, did you... I explained this in the post that was closed. What gets me is that you plead ignorance by your own admission. So tell me, what are you doing even commenting on the topic? I suggest you go and study John Cuthber. I care little for your opinion and whether you are amused or not. Have something to say about the topic, say it. Otherwise I suggest you go play somewhere else...

Some time ago there was a discussion on this topic which was derailed and locked. The following link provides definitive proof that dy/dx is in fact exactly a ratio: http://thenewcalculus.weebly.com/uploads/5/6/7/4/5674177/dydx_compared.pdf

I recently had a discussion at http://www.sciencefo...ied-as-a-ratio/. Although I ended up insulting the individual (Dr. Rocket) who would not cease insulting me, I thought about the entire discussion and wrote up a short document that addresses some key mistakes people make in any bad dialogue. The document is attached. Insults are unpleasant, but in my opinion someone who dishes out insults should learn to take them also. My advice to bullies is: Don't dish it out if you can't take it. In this document I discuss a recent dialogue I had with a physicist at Scienceforums.net. My commentary is in blue font. That is great site for those with a strong stomach and aweak mind. - Dr. Rocket This is never the correct way to start a dialogue with anyone. It is insulting and addresses none of the content it claims is suitable only for weak minds. You will see how this so-called physicist puts his foot in his mouth over and over again. The best way to respond to such a statement is to mirror it because the accuser evidently needs to experience the unpleasant nature of his initial comment. You say a lot of things. Most of them are wrong. - Dr. Rocket Not a civil statement even if it were true. Rather than make such a statement, choose one (or two at most) topic that you think is wrong and address this topic, not the person who made a comment related to the topic. Rocket failed throughout the dialogue to provide even one example of what he thought was wrong. Ironically, almost everything he wrote was wrong. That is evidence of nothing more than a failing on your part. Again, rather than provide evidence of what he claims is wrong, he chooses to attack the person. This is what is commonly known as ad hominem. Many academics are guilty of this type of dialogue. What it shows is that they know very little or are very unsure of their arguments. In Rocket's case this was evident because he constantly accused me of being wrong but never once provided evidence to support his claims. You are missing the point. This comment is disdainful. It's almost as good as a slap in the face. Coming from Rocket who was guilty of this, it was even more obnoxious. Clearly you don't know what I am talking about. But that is not surprising since you don't know what you are talking about either. At this point the gloves are off. Rocket knows he is wrong and tries intimidation but has no idea that it can bite him in the butt. I decided to give Rocket the spanking he deserved, but as you will notice from the dialogue, he did not learn much! Your opinion on the superficiality of the difference is incorrectand evidence of abject ignorance concerning the most important definition inall of mathematics, that of a function. The insults just keep intensifying when I don't play his game and just go away. The use of phrases such as abject ignorance are entirely uncalled for and have no place in any civil dialogue. Individuals such as Rocket can never admit their mistakes. They will first attempt to back out gracefully. I would have allowed this had Rocket not been such an arrogant asshole but I decided to chastise him. A fool should not be allowed to intimidate others. Conclusion: I think one should mirror the behaviour of creeps like Dr. Rocket even if it appears not to have helped. Rocket should not be discussing any topic he knows nothing about as if he is an authority on the same and insulting others who are in fact an authority on the subject.

You don't have my respect because you are a fool. "Your assertion that you have had trouble with "academics" speaks volumes, though I have not been in academia for some time." Where did you read that you moron? Are you delusional as well? "Go learn some mathematics and stop making absurd statements." If only you knew how much this applies to you! Once again, claiming that I make baseless statements is your opinion. People are not stupid. They will realize you are clueless once they read the entire discussion. State where I have made a baseless statement. I don't care for your dishonest opinion. Do tell what the baseless and absurd statements are... Oh wait, there aren't any. You are a lying blowhard. Tsk. Tsk. So far the only baseless and irrelevant statements have been made by you: "Thus you cannot sensibly talk about because the objects that are purportedly being multiplied are functions that do not have a common domain." - Dr. rocket Chuckle, chuckle. The previous statement is wrong, absurd, baseless and irrelevant. ajb: I know what your response will be. Hold it. This is my last post. Yes, yes, I know I have insulted our friend Dr. Rocket. I could not help it. I apologize for my insults but not the mathematics or logic because I am correct. I was pushing Rocket to see what kind of character he has. Evidently he does not have the gumption to admit he is wrong. This is fine with me. I don't really care.

To see how asinine Dr. Rocket's argument is, let's consider p=-a/b q=-b/c r = c/(-a) in ordinary arithmetic (no calculus) Now, according to his argument, he believes that pqr suggests the product is 1 when it is in fact -1. But, p, q and r are symbols. Before we know their values, we can tell the product might be 1 or -1. However, when we substitute the numeric values for the symbols, we know exactly that it is -1. In my New Calculus, the symbolic differentials (whether ordinary or partial) are exactly equal to the antecedent and consequent parts of the finite difference ratio - not Newton's finite difference ratio (because Newton was WRONG), but my finite difference ratio. When the symbols transition to numbers in my finite difference ratio, the differentials are exactly equal or proportional to the antecedent and consequent parts of my finite difference ratio. Dr. Rocket: Until you admit you are wrong, you are no different from most academics I've met and you certainly don't deserve my respect.

Nonsense. It works every time. But just like everything else needs to be carefully considered, this also has to be evaluated within context. Please do not feed Dr. Rocket's huge ego. You are correct. However, his communication to me has been very disdainful, arrogant and provocative. If he were correct, it would probably not be so bad, but he is clearly wrong. All he has to do is admit he is wrong and move on. And I think he knows he is wrong.

"You are missing the point. " I believe you have missed the point and you know it. So you are trying to back out gracefully. "In that octant you can think of the equation as defining y implicitly as function of x and z, or defining x implicitly as a function of y and z or defining z implicitly as a function of x and y -- BUT not all three at the same time. Thus you cannot sensibly talk about [math]\frac{\partial y}{\partial x}\frac{\partial z}{\partial y}\frac{\partial x}{\partial z}[/math] becuse the objects that are purportedly being multiplied are functions that do not have a common domain. " That they have a common domain or nor matters none. In this case they do have a common domain, so you are once again wrong. The domain is (-a,a) for all the partial derivatives. Trying to BS me? I am a mathematician and you do not fool me. This previous sentence is irrelevant. "You can juxtapose the symbols, but the implied multiplication does not make sense, and that is why the "chain rule" does not appear to work here." No, your ideas don't work, because you don't know what you are talking about. Not implied multiplication (no such thing), but exact multiplication takes place. "It all comes back to the simple fact that derivatives and partial derivatives are defined in terms of functions, not equations. " Again, BS! There is only a superficial difference in this case and it makes no difference to our discussion whatsoever. "Clearly you don't know what I am talking about. But that is not surprising since you don't know what you are talking about either" Too funny. I corrected you and I don't know what I am talking about... I am a mathematician and you are evidently not. "A function from a set A to a set B is a subset of the cartesion product AxB such that if (a,x) and (a,y) both belong to that subset then x=y. If (a,x) is a pair in the function then we commonly write x=f(a). An equation is simply a statement that two thing are in fact the same. " Really? You don't say?! I am not inferior to you. Do you think I am unaware of basic facts? Your response is devoid of logic and you are dancing around like a chicken without a head because you know you are wrong. Rather than try to cover up your stupidity, just admit that you are wrong. You claim an "equation is simply a statement that two things are in fact the same". Gee, let me see: f(x,y,z)=3x^5-2z and y=z^2+x^3. Hmm, your statement applies to both the function and the equation. It is clearly irrelevant and you have no idea with whom you are dealing with! Please, no more BS, okay? "Your opinion on the superficiality of the difference is incorrect and evidence of abject ingnorance concerning the most important definition in all of mathematics, that of a function." Actually what shows is your embarrassment at having being corrected. The partial derivative cannot just be meaningless symbols as you claim. For if this were the case, we could not talk about a product at all. Now, I am correcting your wrong comments on this post - you are clearly clueless as to what these partial derivatives or their physical interpretation means. The previous statement is so devoid of truth and evidently false, that it's hard to even know where to start pointing out your lack of understanding or maybe just your refusal to admit you are wrong? Be careful how you respond as my next response to you may include abusive verbal terms regarding your lack of intelligence. I am not inferior to you. In fact I consider myself inferior to no one. The first step toward understanding is to admit you are wrong when you are wrong. And you are wrong here in case you think otherwise. If you are a sincere academic, then what you do is say that you are wrong and move on. Now, if you have any further questions, I will be glad to help you but watch the arrogant and disdainful tone of your communication! The derivative (or partial derivative) is not infinitesimal, has nothing to do with very small values and does not require any knowledge of limits.

Actually, it is completely ill-defined and arose from Cauchy's Kludge which is in error. http://thenewcalculu...auchykludge.pdf

Wrong. See http://mathworld.wol...Derivative.html (don't feel like typing it out, sorry) This is an equation, so I don't know what you are talking about... Besides, what is the difference between a function and an equation? Please define both. As far as I am concerned, the difference is superficial. I see what you mean here but this is due to the fact that you are interpreting the product out of context. The ratios in the product are symbolic so you cannot simply assume that the suggested product is 1 when it is in fact -1. The symbolic ratios become actual ratios when replaced by numbers - this is a part of your inability to understand this difference. A symbolic ratio does not carry a sign in it. I am surprised you missed this! The sign is understood once the ratio transitions from symbol to number. Observe that none of this changes the fact that partial derivatives are proper ratios. They are not infinitesimal (whatever this rot means) nor are limits required. One more thing: If you are going to say I am wrong, please have the decency to tell me where you think I have gone wrong. Just stating your opinion is valueless to me. Who knows, you may yet correct me...

I see no difference on first inspection. But I am not a mind-reader, so I don't know exactly what Dr Rocket is referring to. I do know that partial derivatives are well-defined, but like everything else, one must consider the context and use of the same. This does not mean that one should cease questioning or investigating this knowledge further. Had I accepted the wrong ideas of the infinitesimal concept, I would never have discovered the New Calculus. I have also shown that the base concept (Cauchy's derivative definition) from which the infinitesimal was born is indeed flawed.

Yes.

"That is great site for those with a strong stomach and a weak mind." And I'd say you have a weak mind. "In other words it is a somewhat useful mnemonic that one ought to follow up with rigorous reasoning since the mnemonic can get you into trouble on occasion. " Nonsense. It is well-defined in my new calculus. There is no doubt as to its meaning. "The derivative is not a ratio in the rigorous sense (outside of nonstandard analysis), but as a limit of ratios that reasoning is sometimes useful, so long as you don't get carried away. " Again, not true. The derivative is exactly a ratio. Assuming that x, y and z are not functions of each other, then [math]\frac{\partial y}{\partial x}=2y\frac{\partial y}{\partial x}[/math] (1) [math]\frac{\partial z}{\partial y}=2z\frac{\partial z}{\partial y}[/math] (2) [math]\frac{\partial x}{\partial z}=2x\frac{\partial x}{\partial z}[/math] (3) How is this equal to -1? You are confusing yourself by failing to realize that the symbols are not numbers until numbers are assigned to one or more symbols. Even if x, y and z are functions of each other, your understanding of partial derivatives is still wrong. "The problem here is that [math]x^2+y^2+z^2=a^2[/math] does not define a function of x, y, and z but only gives one in terms of the other when you fix the third variable." Actually, it very much defines a function of x, y, and z. In fact, one can parameterize all of these in terms of a 4th variable. So what you say is false. "Thus without further explanation [math]\frac{\partial y}{\partial x}\frac{\partial z}{\partial y}\frac{\partial x}{\partial z}[/math] is not really meaningful as they cannot all be defined under a single set of assumptions -- partial derivatives are defined for functions, not equations." I am not certain what you mean by "under a single set of assumptions"? There are no assumptions. Partial derivatives are well-defined. The following links explain more: http://thenewcalculu...ing_of_dydx.pdf http://thenewcalculu...ean_exactly.pdf http://thenewcalculu...tes_example.pdf You have to assign a meaning to each partial differential. You can't say dy/dx x dz/dy x dx/dz where the dees are partial derivatives unless you know what these are. It's like saying turkey/dog x cat/turkey x dog/cat = 1. As for checking everything in mathematics, this goes without say.

Here is an interesting link: http://india-men.nin...l-quotient?page One of the attachments called meaning_of_dydx.pdf explains. Another interesting link is: http://thenewcalculus.weebly.com/uploads/5/6/7/4/5674177/lhopital.pdf Non-standard analysis is absolute rot in my opinion. In fact the very concept of infinitesimal is nonsense. Rather than try to explain here, I suggest a visit to my New Calculus site: http://thenewcalculus.weebly.com

Well, thank you. I hope that my account will not be disabled and terminated because I have different views to some of the great mathematicians (Newton, Leibniz and Cauchy). This has happened in the past. You can read a lot about me at: http://thenewcalculus.weebly.com and http://www.researchgate.net/profile/John_Gabriel