Possible proof of Gabriel's Theorem?
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From: David C. Ullrich on 6 Mar 2005 08:46 On 5 Mar 2005 15:56:44 -0800, "Jason" <logamath(a)yahoo.com> wrote: > >So you think I don't know what I am talking about? _every_ competent mathematician reading these threads _knows_ that you don't know what you're talking about. You give proofs of this in just about every post. >Well, you probably >need to study what a riemann integral is and then compare it with >gabriel's average derivative and you will see they are vastly >different. Riemann's integral is a joke next to gabriel's average >derivative. Gabriel does not use a mesh value and gabriel's result if >applied to numeric integration/differentiation yields a far better >result than anything riemann ever dreamt of! In fact the Lebesgue >integral definition is not as strong as gabriel's ATT either. > >See David, you need to do your homework carefully before you continue >to blabber all the junk you have been blabbering out >on this forum. Evidently *you* have no idea what you are talking >about!! Let's think about this. We've "disagreed" about many things. So far there's _one_ question where we disagreed, where finally both sides have agreed on which answer is right: Q: If f' exists everywhere need f' be continuous? A: No. Given that on the _one_ question where the two of us finally agreed it turned out you finally agreed that I was right, do you think you might want to revise any of what you say above? >Jason ************************ David C. Ullrich
From: W. Dale Hall on 6 Mar 2005 12:36 Jason wrote: > So you think I don't know what I am talking about? Well, you probably > need to study what a riemann integral is and then compare it with > gabriel's average derivative and you will see they are vastly > different. Riemann's integral is a joke next to gabriel's average > derivative. Gabriel does not use a mesh value and gabriel's result if > applied to numeric integration/differentiation yields a far better > result than anything riemann ever dreamt of! In fact the Lebesgue > integral definition is not as strong as gabriel's ATT either. > > See David, you need to do your homework carefully before you continue > to blabber all the junk you have been blabbering out > on this forum. Evidently *you* have no idea what you are talking > about!! > > Jason > Jason, I think you forgot to put in that little thing you used to say about not being a supporter of Gabriel's work, but merely are curious about its validity. Here, I'll look it up for you: Disclaimer: I am not endorsing any of Gabriel's work. Neither am I absolutely certain that all of it is correct without any doubt. However, I am interested in his average sum theorem and in particular, a special case of it which leads to what he calls the average tangent theorem (ATT). The ATT (or Average Derivative) if true can be used to prove the mvt and ftoc and several others. There. Now your objectivity is plain for all to see. Dale.
From: MFolz on 6 Mar 2005 20:52 > Riemann's integral is a joke next to gabriel's average > derivative. Gabriel does not use a mesh value I don't claim to be an expert on analysis, nor do I have the time to decipher Gabriel's (pseudo?) math, but the Riemann integral does not necessarily use a mesh value. Most analysis texts these days seem to define the upper integral F as inf U(g,P) and the lower integral f as sup L(g,P). If F=f, then the function g is integrable.
From: Jason on 6 Mar 2005 23:00 Actually, they all use a mesh value. However, the riemann integral is an *approximation*. Gabriel's average tangent/derivative theorem is not an approximation - it is *natural integration*. You can take any definite integral and compute it's value using the average derivative. So you do not have the time to *decipher* gabriel's math yet you question its validity? Strange, I did not know that math needs deciphering for it is either true or false. If you have not looked at something, why do you by default cast doubt on its truth? You are simply following in the footsteps of most fools on this forum. The majority of posts including those by math professors demonstrate they (the real trolls) did not even bother to so much as read gabriel's stuff. All I have seen so far is sheer arrogance, stupidity and the utmost ignorance. Now allow me to critisize your post: > I don't claim to be an expert on analysis, nor do I have the time to > decipher Gabriel's (pseudo?) math, but the Riemann integral does not > necessarily use a mesh value. Most analysis texts these days seem to > define the upper integral F as inf U(g,P) and the lower integral f as > sup L(g,P). If F=f, then the function g is integrable. Most analysis texts are a load of rubbish and are taught by insecure individuals the likes of whom can be found on this forum. What are you trying to say? What does *integrable* mean? It's not an English word. Let's suppose you mean that g is a function and that by *integrable* you mean it can be integrated. So what is P then? Do you think that most people who read this forum know what you mean?
From: Jason on 6 Mar 2005 23:22
One more thing: The father of real analysis was Karl Weierstrass who by the way, did not complete his degree choosing rather to nurture his beer belly and skills in fencing. He was a pathetic drunk whose works were largely ignored a long time. Today, his slippery and vague ideas and concepts are taught in *real analysis*. The use of epsilon-delta arguments is highly questionable for real analysis. Most supporters of real analysis will argue in strong support of no hyperreal numbers existing in *real analysis*, yet the very idea of epsilon-delta assumes real numbers are points defined on a number line. Weierstrass did not put calculus on a firm footing or more robust ground, he confounded most of today's so-called mathematicians who are nothing more than fat, beer bellied drunks who are by nature thugs and slimebags. How can anything sound proceed from an unhealthy mind and a sack of beer? Wow, am I gonna get responses to this!! Sheeesh, I just don't want to think how many trolls are going to jump on their band wagon... Fat and ugly boys like hammick and company are sure to splatter their beer's worth without any doubt. Okay trolls, do your thing... |