lördag 26 oktober 2019 kl. 13:53:35 UTC+2 skrev Eram semper recta:
> On Friday, 25 October 2019 21:43:50 UTC-4, Markus Klyver wrote:
> > I've followed John Gabriel quite a while now, as I find dumb/shitty/cranky math and physics funny.
> Anyone starting a rant with disparaging comments and libel is never taken seriously. Assertions and opinions are ... well, just that - assertions and opinions. Facts are something different.
> > As I know how rude and completely unwilling John Gabriel is to learn anything new, this isn't a response to him.
> Chuckle. Condescension is the first sure sign of insecurity in mainstream academics. It typically goes something like this:
>
> "I've been teaching the derivative for 41 years and so I should know what it means.", Mihalis Lambrou (lam...@math.uoc.gr)
>
> The first thing the idiot Lambrou does is dismiss the fact that
>
> [f(x+h)-f(x)]/h = f'(x)+Q(x,h) where Q(x,h) is some expression in h and/or x.
>
> The problem: The above statement is a FACT. It is not up for debate.
> >
> > I felt, though, that some points has to me made about his (quite elementary) errors on undergrad introductory real analysis:
> Klyver has learned good English, so one must try to rearrange the order of those words before the nonsense can even begin to make sense.
> >
> > 1. The derivative f' of a real function f is the limit of (f(x+h)-f(x))/h as h→0, given the limit exists.
> This is FALSE as I have *proved* over and over again.
>
> f'(x) = [f(x+h)-f(x)]/h - Q(x,h)
>
> NEVER produces the derivative unless you do something really stupid such as discard Q(x,h), but in order to do this in your bogus calculus, you have to set h=0. Your limit hand waving bullshit doesn't cure the problem. It doesn't even address the problem. It's like placing a band-aid on a cut that needs many stitches. Chuckle.
>
> It's like saying: "Look, we know it's nonsense to set h=0, but we'll say that we don't actually do it, even though what we do with limits is EQUIVALENT, because using limits we can show that a **known** derivative exists."
> > Now, Gabriel claims this is ill-defined because generally limits are very hard to calculate.
> Swine! I have never claimed any such thing. I understand limits better than you or anyone else on the planet. You fucking moron! I taught limit theory in my math classes and my students excelled at university because they knew how to separate bullshit from fact. At least, try to acquire the virtue of truth, because cranks like you are known to be liars and libelers.
> > In fact, there is no systematic way to find a general limit.
> WOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>
> How long did it take you to admit this, you pathetic, moronic crank?!!!!
>
> I am still not convinced you get what I am saying, because you left out a keyword "valid" and you are misleading in your choice of words. I say:
>
> There is no **valid** systematic way of finding a derivative (not limit).
>
> It doesn't matter what you call your shit theory - it is still shit.
> >
> > This doesn't mean that the limit is ill-defined.
> It means EXACTLY that the limit is ill defined.
> > I could define x to be the 657566556787686578987965:th prime number, without knowing what x is.
> You could, but reifying x is another story. It is also misleading then to say you don't know what is x because you already one attribute of x, that is, its appearance in the sequence of consecutive prime numbers.
> > I know that a such prime number exists, hence x is well-defined.
> No. Because you have not reified x. Reification means producing the prime number.
> > Similarly for limits, given that the limit exists, it's well-defined.
> Huh? Limits are not like *prime numbers*, you utter moron. There is no similarity whatsoever.
> > In fact, the topological limit in (real) metric spaces is unique, so we can talk about *the* limit.
> There is no connection with your bullshit limit in metric spaces and topology is known to be a bunch of crap with little or no use whatsoever.
> >
> > There is no requirement on actually being able to *compute* something you've defined in order for it to be well-defined:
> I have stated the requirements and a moron like you will abide by my requirements because morons don't get to question subjects beyond their reach:
>
> https://www.linkedin.com/pulse/what-does-mean-concept-well-defined-john-gabriel
> > an other example are integrals. Integrals are generally impossible to compute, and there is no known method or algoritm to calculate an arbitrary integral.
> Bullshit. Definite integrals are computed in a well-defined way using the mean value theorem, as a product of two arithmetic means. Of course, if one has been infected with the rot of infinite rectangles and other crap, then it is impossible.
> > We just know how to do it in very specific cases.
> Rubbish. Any function f' which has a primitive f can be determined in a finite computation, that is, f(b)-f(a) is the integral.
> > Not being able to calculate an integral doesn't mean it's undefined.
> No one said it is undefined, you moron! It may have a limit that is not a number, but some incommensurable magnitude, in which case one use numeric integration and common sense which you so desperately lack.
> >
> > (He doesn't understand integrals either, but I'm too lazy to explain why his "definition" is not a definition.)
> Chuckle. I am the first to prove the mean value theorem constructively and this dimwit claims I don't understand integration. LMAO.
>
> https://drive.google.com/open?id=0B-mOEooW03iLZG1pNlVIX2RTR0E
>
> The fundamental theorem of calculus is derived in one step from the mean value theorem.
> >
> > I'm very surprised that he almost derived the more general definition of the derivative, but stumbled on the the finish line. An equivalent definition for the derivative is that f(x+h)-f(x) = Ah + hρ(h) for some function ρ that will go to 0 whenever h→0. To recover the usual definition, divide both sides with h and let h→0. Then (f(x+h)-f(x))/h = A+ρ(h) → A. This is the natural generalisation and usual definition of partial derivatives.
> This bullshit is all debunked in my free eBook:
>
> https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
>
> <irrelevant drivel in an attempt to prop up theory that has nothing to do with calculus or mathematics>
> > We can think of A as an linear approximation, since when h is small, then ρ(h) will be to (by the definition of a limit).
> >
> > For example, for f(x)= x², we would have ρ(h)=h, which of course goes it zero when h does it.
> >
> > 2. Convergence and limits in metric spaces are things Gabriel repeatably misunderstands. When we define convergence, we do that in a space. What that means is that we already have a space, and try to formalise what it means for something to converge *in that space*.
> >
> > This means there could be metric spaces in which Cauchy sequences do not converge, because we require the limit to be in the metric space. An example would be the partial sums of the decimal expansion of sqrt(2) in the rationals. This forms a sequence not converging, because if it did it would have to be sqrt(2). We can decide to view the same sequence via an inclusion mapping ℚ↪ℝ as metric spaces, in which the same sequence does converge.
> The chief property of Cauchy sequences is that they ALL converge. I don't give a shit to whether they converge to a rational number or an incommensurable magnitude.
>
> sqrt(2) is NOT a number, but a symbol for an incommensurable magnitude. I guess you first have to learn what it means to be a number before you can understand what this means. It doesn't help memorising metric space theory which you don't understand and which is based off number theory that has been validated in certain aspects.
> >
> > Decimal expansions, as I mentioned above, are defined as limits.
> Rubbish. In the mainstream only, they are defined as limits after the ideas of Euler's S = Lim S.
> > More specifically, they are defined to be the limit of the partial sums.. Since the partial sums of a real decimal expansion is Cauchy, they will converge in the real numbers.
> Nonsense which has all been debunked in my free eBook. There is no valid construction of real number - it's a pipe dream. Neither Dedekind Cuts nor classes of equivalent Cauchy sequences are valid constructions.
> > Metric spaces having this property are called complete.
> >
> > One motivation for the real numbers is the completeness.
> It's quite pathetic how mainstream morons introduce terms such as completeness in order to obfuscate the issue at hand. Fact is, completeness has ZERO to do with the issue and I have PROVED this in my first constructive proof of the mean value theorem.
> > Real functions over R also behave nicely, such as obtaining a minimum and maximum on compact sets (w.r.t. the Borel topology generated by open intervals).
> >
> > Many layman texts go over the details of these properties, which is of course why John Gabriel doesn't understand them. Of course: if Gabriel actually read an undergrad textbook in real analysis, he would understand that these properties are not as "deep" and abstract as he think they are.
> Chuckle.
> >
> > 3. His "definition" of numbers makes no sense. He starts off with the concept of a point "as an abstract idea of where you are". This seems to imply a very physical definition, and not something mathematicians would find very satisfying. He the gives a vague explanation of travelling between points (already assuming all sorts of things about how the Euclidean space works, and what velocity is). He then defines "lines" and circles as "distances", ignoring the fact that a distance usually is a *number* and not a path.
> Klyver again misrepresenting and lying about everything I've written. Don't believe a word this moron utters. Read my free eBook. I won't even bother further.
> >
> > Finally, when defining a "number", he already assumes what a magnitude is, which is only vaguely defined as "the size or extent" or something. He mentions lengths, masses and volumes, but these are physical objects. So again: we define something in terms of something that depend on the physical nature, which is not a satisfying definition for a mathematician.
> > He further assumes that these magnitudes exists on their on, but by his own criteria these objects could never be ratified because they simple make no sense. What does it mean to have an abstract magnitude, if you don't realise it in some form of underlying space? Of course, Gabriel doesn't mention the usage of Euclidean space and the implicit axiomatization. The axioms of Euclidean space of course follows as "theorems" if you implicitly assume them.
> >
> >
> > 4. And oh, 3 <--> 5-2 makes no sense since 3 and 5-2 aren't logical statements. A statement can be logically equivalent to an other statement, but it makes no sense to say that a number is logically equivalent to an other number. You can't logically say "5 implies cat". But you can say "if I have 5 cats, I have a cat." This is a logical statement of the form "If x, then y" and it happens to be (always) true.
> >
> > As John Gabriel might read it, I'll give an other example of something that's always false: "If a have no cat, then I have two cats". This statement is formally false, but it still makes logically and formally sense. It's a formal statement which you can evaluate and assign a truth value to. So saying that "x is less or equal to 4" just means that we can check if x satisfies (x strictly less than 4) OR (x=4). This is a logical statement combined made up with two different statements connected with a truth-functional OR. This is the same OR which you encounter in a computer or electronics engineering class. One important difference is, of course, that physical logical gates depend on the physical reality whilst truth functionals are formalised by propositional logic.
> >
> >
> >
> >
> > So in short: above is my selection of favourite parts of what John Gabriel doesn't understand about elementary mathematics (mostly focused on analysis). I'll be very eager to see if he responds to this. Maybe he'll feature me in one video, it's quite comical to be called an ape by a crank.
> Klyver is an ape and what bothers him the most is that it comes from someone (ME) who is far superior to him intellectually. I have already debunked all Klyver's objections and rants.
>
> This will be the ONLY response Klyver gets on sci.math and it was not for his edification! You can't fix ape. Chuckle.
Stil haven't addressed a thing.