> > "PoorRichard" <poorrichar...@hotmail.com> wrote in message <news:wU5f9.3190$i84.1200@fe02>... > > > I have the book. The chapter you point out discusses the shaky foundations > > > upon which the calculus was initially developed. But things worked, so > > > mathematicians swept some issues under the rug, for a while. Things changed > > > in the 19th century.
> > > You should read: The History of the Calculus & its Conceptual Development by > > > Boyer [ISBN: 0-486-60509-4]
> > I remember reading the book on calculus by Richard Currant, many years > > ago. Still remember the paragraph on 'shaky foundations of calculus' > > and that as a matter of fact it was a tremendous luck for the whole > > history of mathematical development that - as you've said ' > > mathematicians swept some issues under the rug', for a while of > > course. > > I also remember reading something like 'why the ancient Greeks haven't > > developed the calculus?' the answer is that their way of thinking was > > mostly axiomatic and systematic type, very logical, very methodical, > > very precise. Calculus on the other hand was developed primarily as a > > result from 'pressure from the real world', like the necessity to > > calculate the volumes'.
> As I recall, Osgoode complained that the > differential was a ghost of a disappearing > quantity, or some such. I think the main > problem the ancients would have had with > calculus is their reluctance to admit even > a formal actual infinity. They preferred to > venture only to potential infinity.
> You might also like the book Mathematics, > the Loss of Certainty by Morris Kline. > Patrick Bertrand Russell wrote: "Pure mathematics is a subject in which we
never know what we are talking about nor whether what we are saying is true." To be sure that what we are saying is true, in applied mathematics, we make the simplifying assumption: 'All units are homogeneous or uniform, continuous and consistent.' It means at all levels of measurement 'a' thing (say X) is an element of itself (or X). It is like saying that 'a set of potatoes is a potatoe.' Such an assumption is necessary in pure mathematics and in physics because if we divide the thing by length (area or vulume) or by time, no one should be able to prove the method or the result wrong. When we say that unit is uniform, continuous and consistent it means X=F(dX)- X has spatiotemporal contiguity and homogeneity. In theory we must use a 'quantum' and number of quanta to specify a given quantity of the thing that satisfies the condition X=F(dX) The first differential of X or what we call as 'dX' can never have any numerical value. All number (X or Y or a or b) used in pure mathemtics must have this characteristic. Therefore these numbers cannot be used in differential calculus. There is one more possibility: The 'unit' cannot be described as Y=F(dY) but Y has mathematical order (other than homogeneity) within it. It means dY=F(Y) but Y is not a function of dY. Here dY is not a constant; it is level of activity like velocity, frequency, tempreature, stress, strain etc. during state of change or acceleration. In this case integral of dY has to occupy either space (like a gravitational field) or time (natural radioactive decay) or both space and time (like uniform linear acceleration). Any number of successive differentiation of Y (described here) will not produce a constant. Y is like a logarithmic scale. Y is a system (like a field) whose behaviour can be predicted with absolute certainty and zero error but the system itself is holistic and has no parts - it is a space-time continuum. The third type of numbers is integers or whole numbers that we use to count spatio-temporally disjointed entities like colored beads or billiared balls. This type of number is only useful in set theory. I believe that there cannot be a 'number' that a mathematician can integrate as well as differentiate at his will. Differential and integral calculi are definitely questionable.
Marco Nelissen <marc...@xs4.xs4all.nl> wrote: > josX <jo...@mraha.kitenet.net> wrote: >> I have no such habbit. In fact, i reply to everything.
> Then please answer each of these questions: > - where is the proof that your TV is a mind control device? > - where is the proof that aliens from Zeta exist?
Note that several days later, and despite his claim that he replies to everything, Jos still hasn't provided us with proof that his TV is a mind control device, or that aliens from Zeta exist... How about it, Jos? Any evidence forthcoming?
> > I also remember reading something like 'why the ancient Greeks haven't > > developed the calculus?' the answer is that their way of thinking was > > mostly axiomatic and systematic type, very logical, very methodical, > > very precise. Calculus on the other hand was developed primarily as a > > result from 'pressure from the real world', like the necessity to > > calculate the volumes'.
The pressure from the real world for calculus was to calculate *pressure*. The Greeks could do *volumetric* calculations even before Euclid came along.
Which is also why that Einstonians are often reminded that they really should take some refresher courses in *calculus* before they do stupid things like pretend that they understand *geometry*, and also accordingly making completed Goedelian asses of themselves.
On 10 Sep 2002 20:29:19 GMT, Marco Nelissen <marc...@xs4.xs4all.nl> wrote:
>Marco Nelissen <marc...@xs4.xs4all.nl> wrote: >> josX <jo...@mraha.kitenet.net> wrote: >>> I have no such habbit. In fact, i reply to everything.
>> Then please answer each of these questions: >> - where is the proof that your TV is a mind control device? >> - where is the proof that aliens from Zeta exist?
>Note that several days later, and despite his claim that he replies >to everything, Jos still hasn't provided us with proof that his TV >is a mind control device, or that aliens from Zeta exist... >How about it, Jos? Any evidence forthcoming?]
I check up on this thread every day or so, and he hasnt replied to what i posted about the quasar he mentioned. Then again, he hasnt brouht it up again. Mabey he is learning.
Eric Gisse <[REMOVE]ks...@uas.alaska.edu> wrote: >On 10 Sep 2002 20:29:19 GMT, Marco Nelissen <marc...@xs4.xs4all.nl> >wrote: >>Marco Nelissen <marc...@xs4.xs4all.nl> wrote: >>> josX <jo...@mraha.kitenet.net> wrote: >>>> I have no such habbit. In fact, i reply to everything.
>>> Then please answer each of these questions: >>> - where is the proof that your TV is a mind control device? >>> - where is the proof that aliens from Zeta exist?
>>Note that several days later, and despite his claim that he replies >>to everything, Jos still hasn't provided us with proof that his TV >>is a mind control device, or that aliens from Zeta exist... >>How about it, Jos? Any evidence forthcoming?]
>I check up on this thread every day or so, and he hasnt replied to >what i posted about the quasar he mentioned. Then again, he hasnt >brouht it up again. Mabey he is learning.
What did you brought up Eric. I don't respond to garbage but maybe it slipped. (This is about the gasjet observed to be going out from Quasar 3C273 at 25 ly in 3 years, disproving SR's speed limit.) -- jos
Herman Trivilino <physh...@kingwoodREMOVECAPScable.com> wrote: >"Eric Gisse" <[REMOVE]ks...@uas.alaska.edu> wrote ... >> See what you have been missing, sci.math. >Thanks. It's no surprise, but it does verify that JosX suffers from the >same syndrome we ocasionally see at the local community college where I >teach. Success at a community college is the last chance. If you can't >make it there you can't make it anywhere ... >> >>>>Taken nad passed any Calculs-level classes? >> >>>Calculus has errors in it's leading chapters (axioms), first fix those >> >>>then i migth bother. >Here's the syndrome in a nutshell: The student can't pass the course, the >source of the problem is either internal (a fault of the student) or >external (a fault of something other than the student). JosX chooses the >latter, choosing the subject matter itself, along with everyone who claims >to understand it or teach it, as the external agent responsible for his >failures.
I do not believe you have it right. He seems rather to be a not atypical product of our miseducational system, where what is taught is by memorization and regurgitation or by excessive drill, such as doing myriads (literally) of addition and multiplication problems.
He also seems to have come through a program where invented spelling and "creative" writing were emphasized. So while he might be able to memorize hundreds of calculus rules and plug into them, that is all he can do in it. He might do well at conversational Japanese, but not with any kind of grammar.
He does not want to know why, but just wants to imitate a machine, and do things by reflex.
>Here's my prediction: At the college he attended he had a reputation for >criticizing, in some detail, every aspect of the professors he could think >of, including appearance. He has similar academic problems with language >skills courses (evident from the way he writes) and blames those problems >on something external to himself as well. He is either on mood-altering >medication now, or will need to be at some point in his life. Otherwise, >his dysfunction will continue to interfere with his ability to have >friends, a family life, and a job.
-- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
In article <54187164.0209090952.18250...@posting.google.com>,
Thinh Tran <thinhvant...@cs.com> wrote: >The problem with math is real, and it is not my statement. For >example, read: >Mathematics - The loss of certainty, Morris Kline, Oxford University >Press 1980. >According to the cover of the book, Dr. Kline was the late Professor >Emeritus of Mathematics, the Courant Institute of Mathematical >Sciences, University of New York. >The problems with the axioms of Calculus is covered in the Chapter >"The Illogical Development: The Morass of Analysis" pp 127-152. >Basically the concept of differentials (e.g., dx) is of great suspect, >and no one has been able to make Calculus rigorous.
The concept of differentials is tricky, but they can be made quite rigorous, not as in most calculus books. I use them quite a bit with matrices.
Calculus was made rigorous by Bolzano in 1817, but most do not get it until after they have done lots of calculations. It is my experience that, except for the small group which can reject the sloppy way they have been taught and operate conceptually, with purely abstract concepts, they keep at being sloppy, Kline falls into this category; classical analysts often do. Newton and Euler were quite aware that their understanding of mathematics lacked the clarity of geometry which started from the Euclidean foundations, but others did not care. BTW, I totally rejected the idea that "geometric intuition" was needed, as while mine is not that bad, I was already using logical intuition instead to greater advantage.
Even with the clumsy present methods, limits are needed to understand "infinite" decimals, such as the expansion for sqrt(2). But algebraic notation and precision belong early, and anyone who has difficulty with induction cannot understand the integers.
-- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
Herman Rubin wrote: > I do not believe you have it right. He seems rather to be a > not atypical product of our miseducational system, where what > is taught is by memorization and regurgitation or by excessive > drill, such as doing myriads (literally) of addition and > multiplication problems.
> He also seems to have come through a program where invented > spelling and "creative" writing were emphasized. So while he > might be able to memorize hundreds of calculus rules and plug > into them, that is all he can do in it. He might do well at > conversational Japanese, but not with any kind of grammar.
Well, on the one hand josX is Dutch and English is not his native language. The "system" he came through is the Dutch one.
On the other hand, the fact that he doesn't correct things even after they are repeatedly pointed out is one more indicator that he doesn't actually read what people say.
josX <jo...@mraha.kitenet.net> wrote: > Eric Gisse <[REMOVE]ks...@uas.alaska.edu> wrote: >>On 10 Sep 2002 20:29:19 GMT, Marco Nelissen <marc...@xs4.xs4all.nl> >>wrote: >>>Marco Nelissen <marc...@xs4.xs4all.nl> wrote: >>>> josX <jo...@mraha.kitenet.net> wrote: >>>>> I have no such habbit. In fact, i reply to everything.
>>>> Then please answer each of these questions: >>>> - where is the proof that your TV is a mind control device? >>>> - where is the proof that aliens from Zeta exist?
>>>Note that several days later, and despite his claim that he replies >>>to everything, Jos still hasn't provided us with proof that his TV >>>is a mind control device, or that aliens from Zeta exist... >>>How about it, Jos? Any evidence forthcoming?]
>>I check up on this thread every day or so, and he hasnt replied to >>what i posted about the quasar he mentioned. Then again, he hasnt >>brouht it up again. Mabey he is learning.
> What did you brought up Eric. I don't respond to garbage but maybe > it slipped. (This is about the gasjet observed to be going out from > Quasar 3C273 at 25 ly in 3 years, disproving SR's speed limit.)
>"PoorRichard" <poorrichar...@hotmail.com> wrote in message <news:wU5f9.3190$i84.1200@fe02>... >> I have the book. The chapter you point out discusses the shaky foundations >> upon which the calculus was initially developed. But things worked, so >> mathematicians swept some issues under the rug, for a while. Things changed >> in the 19th century. >> You should read: The History of the Calculus & its Conceptual Development by >> Boyer [ISBN: 0-486-60509-4] >I remember reading the book on calculus by Richard Currant, many years >ago. Still remember the paragraph on 'shaky foundations of calculus' >and that as a matter of fact it was a tremendous luck for the whole >history of mathematical development that - as you've said ' >mathematicians swept some issues under the rug', for a while of >course. >I also remember reading something like 'why the ancient Greeks haven't >developed the calculus?' the answer is that their way of thinking was >mostly axiomatic and systematic type, very logical, very methodical, >very precise. Calculus on the other hand was developed primarily as a >result from 'pressure from the real world', like the necessity to >calculate the volumes'.
I disagree. They were not always that precise, and many of their "proofs" used intuitive ideas. Archimedes found a way to justify the arc length of a circle, and of many other curves, and his favorite theorem was that the area of a zone of a sphere is the same as the areas cut out on a cylinder tangent to the sphere and perpendicular to the cutting planes of the zone. Surface area was not put on the sound foundation which arc length reached in the 19th century until near the mid 20th century.
I believe the big problem was the lack of adequate notation for variables and functions. For numerical quantities, Diophantus introduced one variable symbol around 300 CE, and it was not until the late 16th century that flexible notation adequate to describe graphs existed.
BTW, the Greeks understood integration to compute areas and volumes, as well as limits, although they could not have given a formal definition of them. The directrix, given in our notation as y = \theta*(\pi/2), x = y*cot(\theta), they knew to approach the point 2/\pi on the X-axis.
-- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
> I believe the big problem was the lack of adequate notation > for variables and functions. For numerical quantities, > Diophantus introduced one variable symbol around 300 CE, > and it was not until the late 16th century that flexible > notation adequate to describe graphs existed.
If we are talking about why the Greeks didn't take the method of exhaustion, for example, & put it all together in what we call the calculus, the reasons are fairly clear. Notation may have been a hindrance but the main reasons were the Greeks lack of a well defined number system & their not having the notion of a convergent infinite series & sequence. While it was obvious to them that one could make the error as small as possible, that did not enable them conceptually go from a finite process to an infinite one, in the sense of limit.
>Eric Gisse <[REMOVE]ks...@uas.alaska.edu> wrote: >>On 10 Sep 2002 20:29:19 GMT, Marco Nelissen <marc...@xs4.xs4all.nl> >>wrote: >>>Marco Nelissen <marc...@xs4.xs4all.nl> wrote: >>>> josX <jo...@mraha.kitenet.net> wrote: >>>>> I have no such habbit. In fact, i reply to everything.
>>>> Then please answer each of these questions: >>>> - where is the proof that your TV is a mind control device? >>>> - where is the proof that aliens from Zeta exist?
>>>Note that several days later, and despite his claim that he replies >>>to everything, Jos still hasn't provided us with proof that his TV >>>is a mind control device, or that aliens from Zeta exist... >>>How about it, Jos? Any evidence forthcoming?]
>>I check up on this thread every day or so, and he hasnt replied to >>what i posted about the quasar he mentioned. Then again, he hasnt >>brouht it up again. Mabey he is learning.
>What did you brought up Eric. I don't respond to garbage but maybe >it slipped. (This is about the gasjet observed to be going out from >Quasar 3C273 at 25 ly in 3 years, disproving SR's speed limit.)
Since you seem to be rather retarded, i will post again so its eazy to find.
Riddle me this. If one gas jet is exceeding c, why isnt the other going c also?
You will write off my references as fuzzbabble and handwave again, but its fun to watch you wiggle when presented with math.
~~~~~~
>>We had supersonic bullets in the mid 20th century, did we not? What >>goes faster than light? Nothing. I welcome experimental proof of >>something otherwise.
>Glad you asked: >Gasjet from Quasar 3C273 has traveled a distance of 25 lightyears in >8 years.
Eric Gisse <[REMOVE]ks...@uas.alaska.edu> wrote: >On 11 Sep 2002 08:00:11 GMT, jo...@mraha.kitenet.net (josX) wrote: >>Eric Gisse <[REMOVE]ks...@uas.alaska.edu> wrote: >>>On 10 Sep 2002 20:29:19 GMT, Marco Nelissen <marc...@xs4.xs4all.nl> >>>wrote: >>>>Marco Nelissen <marc...@xs4.xs4all.nl> wrote: >>>>> josX <jo...@mraha.kitenet.net> wrote: >>>>>> I have no such habbit. In fact, i reply to everything.
>>>>> Then please answer each of these questions: >>>>> - where is the proof that your TV is a mind control device? >>>>> - where is the proof that aliens from Zeta exist?
>>>>Note that several days later, and despite his claim that he replies >>>>to everything, Jos still hasn't provided us with proof that his TV >>>>is a mind control device, or that aliens from Zeta exist... >>>>How about it, Jos? Any evidence forthcoming?]
>>>I check up on this thread every day or so, and he hasnt replied to >>>what i posted about the quasar he mentioned. Then again, he hasnt >>>brouht it up again. Mabey he is learning.
>>What did you brought up Eric. I don't respond to garbage but maybe >>it slipped. (This is about the gasjet observed to be going out from >>Quasar 3C273 at 25 ly in 3 years, disproving SR's speed limit.)
>Since you seem to be rather retarded, i will post again so its eazy to >find.
>Riddle me this. If one gas jet is exceeding c, why isnt the other >going c also?
Come again ? What "other gasjet" ?
>You will write off my references as fuzzbabble and handwave again, >but its fun to watch you wiggle when presented with math. >~~~~~~
It's not me doing the wiggling and evading/ignoring.
>>>We had supersonic bullets in the mid 20th century, did we not? What >>>goes faster than light? Nothing. I welcome experimental proof of >>>something otherwise.
>>Glad you asked: >>Gasjet from Quasar 3C273 has traveled a distance of 25 lightyears in >>8 years.
>Are these people wrong? I know your awnser, so why are they wrong?
Is this the "close to the line-of-sight fuzzbabble explanation" ? Why don't you quote your links, i have more to do that investigate blabla shill sites for the SRists. -- jos
PoorRichard <poorrichar...@hotmail.com> wrote: >"Herman Rubin" <hru...@odds.stat.purdue.edu> wrote in message >news:alnptu$2ppi@odds.stat.purdue.edu... >> I believe the big problem was the lack of adequate notation >> for variables and functions. For numerical quantities, >> Diophantus introduced one variable symbol around 300 CE, >> and it was not until the late 16th century that flexible >> notation adequate to describe graphs existed. >If we are talking about why the Greeks didn't take the method of exhaustion, >for example, & put it all together >in what we call the calculus, the reasons are fairly clear. Notation may >have been a hindrance but the main reasons were the Greeks lack of a well >defined number system & their not having the notion of a convergent infinite >series & sequence. While it was obvious to them that one could make the >error as small as possible, that did not enable them conceptually go from a >finite process to an infinite one, in the sense of limit.
They did have the idea of limit, and did realize that area is the integral of height, but AFAIK only computed integrals of quadratics and of sqrt(x). I still think that something as simple as algebraic notation would have bridged the gap.
There was nothing wrong with their number system for positive integers. It was the standard decimal system with different symbols for multiples of the different powers of 10, but this is not that much of a difference. Notice that exponentials and logarithms, and the integrals of general positive rational powers, all precede calculus. These started around 1600, with the general use of variables by Viete in the 16th century, and the subsequent analytic geometry of Descartes.
-- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
From what I have read & understand about Greek mathematics, I would have to say that I don't agree with your above stated view & that it is not the prevailing one amongst those who study this seriously. What are you basing your statement on? I am _not_ an expert on Greek mathematics, I can only go by what 'the authorities' say & what I can read in translation. I unfortunately do not know the Greek language so as to personally verify such views.
> There was nothing wrong with their number system for positive > integers. It was the standard decimal system with different > symbols for multiples of the different powers of 10, but this > is not that much of a difference. >
This is from Boyer:
"The method of exhaustion, although equivalent in many respects to the type of argument now employed in proving the existence of a limit in the differential an integral calculus, does not represent the point of view involved in the passage to the limit. The Greek method of exhaustion, dealing as it did with continuous magnitude, was wholly geometrical, for there was at the time no knowledge of an arithmetical continuum. This being the case, it was of necessity based on notions of the continuity of space-intuitions which denied any ultimate indivisible portion of space, or any limit to the divisibility in thought of any line segment. The inscribed polygon could be made to approach the circle as nearly as desired, but can never become the circle, for this would imply an end in the process of subdividing the sides. However, under the method of exhaustion it was not necessary that the two should ever coincide. By argument based upon the reductio ad absurdum, it could be shown that a ratio greater or less than that of equality was inconsistent with the principal that the difference could be made a small as desired.
The argument of Eudoxus appealed at every stage to intuitions of space, and the process of subdivision made no use of such unclear conceptions as that of a polygon with infinite number of sides-that is, of a polygon which should ultimately coincide with the circle. No new concepts were involved, and the gap between the curvilinear and rectilinear still remained unspanned by intuitions."
And later, on the work of Archemeides;
"...this is, of course, exactly the method of proof for the existence of a limit, but Archimedes did not so interpret the argument. He did not express the idea that there is no remainder of a limit, or that the infinite series is rigorously equal to (4/3)A. Instead, he proved, by the double reductio ad absurdum of the method of exhaustion, that the area of the parabolic segment could be neither greater nor less than (4/3)A. In order to be able to define (4/3)A as the sum of the infinite series, it would have been necessary to develop the general concept of real number. Greek mathematicians did not possess this, so that for them there was always a gap between the real (finite) and the ideal (infinite).
It is not strictly correct, therefore, to speak of Archimedes' geometrical procedure as a passage to the limit, for the essential part of the definition of a limit is the infinite sequence. Inasmuch as he did not invoke the limit concept, it is hardly correct to say that in finding the sum of such series Archimedes answered in a very explicit in definite manner some of the difficult questions raised by Zeno...
The notion of the limit of an infinite series is essential for the clarification of the paradoxes; but the Greek mathematicians (including Archimedes) excluded the infinite from their reasoning.The reasons for this ban are obvious: intuition could at the time afford no clear picture of it, and it had as yet no logical basis. The latter difficulty having been removed in the 19th-century and the former being now considered irrelevant, the concept of infinity has been admitted freely into mathematics. The related limit concept is now invoked in the explication of the paradoxes, as well as in a simplification of Archimedes long indirect demonstrations."
Pages 34-35 & 51-52
"The History of the Calculus..." by Boyer. {Great source of other references on this topic too}
>>Riddle me this. If one gas jet is exceeding c, why isnt the other >>going c also?
>Come again ? >What "other gasjet" ?
There are two. One along each axis.
How fast is the other one going, jos?
>>You will write off my references as fuzzbabble and handwave again, >>but its fun to watch you wiggle when presented with math. >>~~~~~~
>It's not me doing the wiggling and evading/ignoring.
Dumbshit.
<snip>
>Is this the "close to the line-of-sight fuzzbabble explanation" ? >Why don't you quote your links, i have more to do that investigate >blabla shill sites for the SRists.
Didnt even read the links. I give up. You are functionaly retarded. You cannot recognise your limits or your ignorance. You are fucking stupid. Every day i read the responses to your retardness and are simply amazed that a human with a brain in his head could be so dense.
You do not want to learn, you have predetermined what you want to see. Just shut the fuck up and keep your preconcieved notions to yourself. You and your fucking conspiracy theorys.
While you continue parroting on about how wrong SR is without any reasons that stand questioning, i will be learning of what you will not learn. Calculus, SR, philosophy, and i will be laughing at you whenever i see you shit and show it to everyone on this newsgroup.
hru...@odds.stat.purdue.edu (Herman Rubin) wrote in message <news:alnjif$2v9o@odds.stat.purdue.edu>... > In article <54187164.0209090952.18250...@posting.google.com>, > Thinh Tran <thinhvant...@cs.com> wrote: > >The problem with math is real, and it is not my statement. For > >example, read:
> >Mathematics - The loss of certainty, Morris Kline, Oxford University > >Press 1980.
> >According to the cover of the book, Dr. Kline was the late Professor > >Emeritus of Mathematics, the Courant Institute of Mathematical > >Sciences, University of New York.
> >The problems with the axioms of Calculus is covered in the Chapter > >"The Illogical Development: The Morass of Analysis" pp 127-152. > >Basically the concept of differentials (e.g., dx) is of great suspect, > >and no one has been able to make Calculus rigorous.
> The concept of differentials is tricky, but they can be > made quite rigorous, not as in most calculus books. I > use them quite a bit with matrices.
> Calculus was made rigorous by Bolzano in 1817, but most > do not get it until after they have done lots of > calculations. It is my experience that, except for the > small group which can reject the sloppy way they have > been taught and operate conceptually, with purely > abstract concepts, they keep at being sloppy, Kline > falls into this category; classical analysts often do. > Newton and Euler were quite aware that their > understanding of mathematics lacked the clarity of > geometry which started from the Euclidean foundations, > but others did not care. BTW, I totally rejected the > idea that "geometric intuition" was needed, as while mine > is not that bad, I was already using logical intuition > instead to greater advantage.
> Even with the clumsy present methods, limits are needed to > understand "infinite" decimals, such as the expansion for > sqrt(2). But algebraic notation and precision belong > early, and anyone who has difficulty with induction cannot > understand the integers.
I will exercise an open mind. Could you describe briefly Bolzano's idea (like an abstract of his idea.) Personally I have read a lot on the subject but am not aware of Bolzano's work. Thanks. Thinh Tran (http://www.thinhtran.com)
jo...@mraha.kitenet.net (josX) wrote in message <news:alk5p3$ok7$8@news1.xs4all.nl>... > TB wrote: > >"josX" <jo...@mraha.kitenet.net> wrote in message > >news:alijqj$30a$3@news1.xs4all.nl... > ><snip> > >> >Good luck JoeX but stay the hell away from people who really care about > >> >quality.
> >> very amuzing all this talk
> >> I made this rhyme for ya'll: > >> You guys only gall,
[...etc...]
There once was a Lim'rick in Math; But this isn't it. This isn't any kind of poem at all. It doesn't even rhyme. Sorry.
>>>You will write off my references as fuzzbabble and handwave again, >>>but its fun to watch you wiggle when presented with math. >>>~~~~~~
>>It's not me doing the wiggling and evading/ignoring.
>Dumbshit.
><snip>
>>Is this the "close to the line-of-sight fuzzbabble explanation" ? >>Why don't you quote your links, i have more to do that investigate >>blabla shill sites for the SRists.
>Didnt even read the links. I give up. You are functionaly retarded. >You cannot recognise your limits or your ignorance. You are fucking >stupid. Every day i read the responses to your retardness and are >simply amazed that a human with a brain in his head could be so dense.
Same here. c'=c+v, and they can't even use it or understand what it might mean. Meanwhile waterwaves go at w'=w+v, soccerballs go at s'=s+v, everything goes at x'=x+v. But using the math? oh no, no fuzzfactor, no game.
>You do not want to learn, you have predetermined what you want to see. >Just shut the fuck up and keep your preconcieved notions to yourself. >You and your fucking conspiracy theorys.
>While you continue parroting on about how wrong SR is without any >reasons that stand questioning, i will be learning of what you will >not learn. Calculus, SR, philosophy, and i will be laughing at you
^^^^^^^^^^^
See? These people do not belong here. SR should be physics, very far removed from philosophy, but unsuprisingly you put them right after one another, how come.
>whenever i see you shit and show it to everyone on this newsgroup.
con...@biosys.net (Big Bird) wrote: >jo...@mraha.kitenet.net (josX) wrote in message <news:alk5p3$ok7$8@news1.xs4all.nl>... >>TB wrote: >>>"josX" <jo...@mraha.kitenet.net> wrote in message >>>news:alijqj$30a$3@news1.xs4all.nl... >>><snip> >>>>>Good luck JoeX but stay the hell away from people who really care about >>>>>quality.
>>>>very amuzing all this talk
>>>>I made this rhyme for ya'll: >>>>You guys only gall,
>[...etc...]
>There once was a Lim'rick in Math; >But this isn't it. >This isn't any kind of poem at all. >It doesn't even rhyme. >Sorry.
It doesn't rhyme but that's just fine define c' = c + v and rationality comes unto thee why don't ye come oh searching student and interpret data so much more prudent then our SRists would ever do you would've found a worthy clue -- jos
In article <3D7F5AA4.43412...@atl.lmco.com>, Randy Poe <r...@atl.lmco.com> wrote:
>Herman Rubin wrote: >> I do not believe you have it right. He seems rather to be a >> not atypical product of our miseducational system, where what >> is taught is by memorization and regurgitation or by excessive >> drill, such as doing myriads (literally) of addition and >> multiplication problems.
>> He also seems to have come through a program where invented >> spelling and "creative" writing were emphasized. So while he >> might be able to memorize hundreds of calculus rules and plug >> into them, that is all he can do in it. He might do well at >> conversational Japanese, but not with any kind of grammar.
>Well, on the one hand josX is Dutch and English is not his native >language. The "system" he came through is the Dutch one.
<snip>
[light bulb over emoticon's colon :-)] Now I understand.
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