Galileo's Paradox
in [Math]
|
From: imaginatorium on 8 Dec 2006 23:22 Tony Orlow wrote: > Lester Zick wrote: > > On Tue, 05 Dec 2006 11:53:13 -0500, Tony Orlow <tony(a)lightlink.com> > > wrote: > > > > [. . .] > > > > You know, Tony, I got to thinking last night... Oh dear, that was Lester... <snip> > > Now there is actually a precedent in conventional mathematics for this > > situation. With complex numbers you actually have two component > > numbers: one conventional algebraic and one imaginary. Thus we can't > > say that r+ni is actually larger than r unless n is even. > > That's true,... Is it? One can't say that r+i is larger than r, but we can say that r+2i _is_ larger than r. I'm totally baffled by this, and wonder if you can explain to us mathematikers what Lester is on about now? > > ~v~~ > 01oo Woof! Brian Chandler http://imaginatorium.org
From: David Marcus on 9 Dec 2006 01:25 Eckard Blumschein wrote: > On 12/7/2006 3:57 PM, David Marcus wrote: > > Lots of people have trouble with math. > > Neither HvH nor I. > > > That doesn't mean > > there is something wrong with mathematics. > > What is wrong in mathematics? > Good question. > > First of all I see mounting evidence for a lack of evidence which could > support some bizarre fancies related to the elusory belief introduced by > Dedekind, Cantor, et al. "there must be more reals than rationals > because the latter are a subset of the former" > > Secondly, I got the impression that the praiseworthy intention to get > more rigorous led to inappropriate pseudo-basic theories because some > basic questions are not yet correctly understood. > > What about the misleading intermediate values, I see them one more > indication for side-effects of incorrect basics. > > > > >> >> >> I do not criticize FT but the integral tables, and I did not have a > >> >> >> problem myself but I recall several reported cases of unexplained error > >> >> >> by just the trifle of two. The integral tables suggest using the > >> >> >> intermediate value. > >> >> > > >> >> > You are criticizing integral tables? > >> >> > >> >> Some of them are rather eclectic and difficult to overlook. Others are a > >> >> bit slim. Sometimes the intermediate values are given, sometimes they > >> >> are omitted which i consider the better decision. > >> > > >> > I haven't a clue why you think integral tables have any relevance to set > >> > theory. > >> > >> The intermediate values, given in integral tables "for mathematical > >> reasons", are misleading and perhaps unnecessary. > > > > No idea what "mathematical reasons" these are. Please give a full quote > > where the book says what the "mathematical reasons" are. > > Sorry, I was not given a book where this was to read but it was simply > repetitiously said to me. I am already happy if people are ready to > utter so frankly what made them sceptical. > > In this case it is pretty understandable what they meant: A function > like y=sign(x) has to have just one value y for every value of x. > If I hide my daring smile and ask if |sign(0)|=1 might be correct, than > people wonder why I have such a silly idea. > > > >> The "mathematical > >> reasons" relate to the somewhat inappropriate arbitrarily distorted > >> notion of real numbers adapted to the illusion by Dedekind and Cantor, > >> real numbers and infinity are numbers with full civil rights. > > > > You really should learn to speak concretely. Telling us what they > > "relate to" tells us nothing, especially since the rest of your sentence > > just contains your usual prejudiced, uninformed rant. > > My point is: Not just irrational numbers but all real numbers are > categorically different from rational numbers. D. & C. declared infinity > and the belonging irrational as well as real numbers numbers with "full > civil right within the kingdom of numbers". In more scientific words: > They denied the categorical difference. This denial was demanded from > mathematical practice and it was reasonable to some extent. Kronecker > did not understand that. He was correct, in principle, when he declared > irrational numbers no numbers at all. More wise views already by > Galilei, Spinoza, Leibniz, Gauss, etc. were ignored. I would like to > follow Leibniz who considered irrationals as fictions with a fundamentum > in re. Do not get me wrong. I never suggestet to numerically operate > with really real numbers. As Peirce wrote, they are mere potentialities. > They must not have full numerical addresses. Otherwise they are rational > numbers. Do not confuse these reals with the reals according to the > still mandatory definitions. The latter are strictly speaking rationals > with as many decimals as you like. You will perhaps already understand > that there is a categorical borderline between the world of numbers and > the world of continuum. Really real "numbers" belong to the continuum > and have different properties. They are not countable. Mathematicians > learned that this means: there is no bijection to the set of naturals. > This is correct but it can also be explained quite simply: The continuum > is smooth. It does not have outstanding points. Single out of the > imagined actually infinite amount of reals do not have any significance. > > > > >> >> >> Experienced mathematicians should indeed know that > >> >> >> they must avoid this use. Some tables give the intermedite value for the > >> >> >> sake of putative mathematical correctness. > >> >> > > >> >> > Please give an example. > >> > >> A gave > >> http://iesl.et.uni-magdeburg.de/~blumsche/M283.html > > > > That link produces a page saying the search didn't produce any results. > > > I see a typo: iesl should read iesk, try again > http://iesk.et.uni-magdeburg.de/~blumsche/M283.html > > The pertaining calculation is easily to find. > > > >> >> I just have my old Bronstein-Semendjajew Teubner 1962 at hand. > >> >> On p. 351, number 13 does not give intermediate values, number 15 does. > >> > > >> > Please quote the entire example. Not everyone is next to a library. > >> > >> No. 15: Integral from 0 to oo dx over sin x cos x / x = > >> = pi/2 for |a|<1 > >> = pi/4 for |a|=1 (intermediate value) > >> = 0 for |a|>1 > > > > There is no "a" in int_0^oo sin x cos x / x. > > > >> No. 13: just over tan(ax)/x > > > > Huh? > > Integral ... like 15 but no intermediate value given, perhaps 13 and 15 > were quoted from different sources. > > >> >> >> Others omit it. > >> >> >> As long as one knows the result in advance, there is almost not risk. FT > >> >> >> and subsequent IFT may perform an ideal check of set theory. > >> >> > > >> >> > What do you mean "ideal check of set theory"? > >> >> > >> >> Set theory leads to intermediate values. > >> > > >> > What do you mean? Do try to be specific. > >> > >> Set theory considers real numbers to be existing numbers, not just > >> fictions. > > > > Nonsense. The words "existing" and "fictions" are your own creation. > > Christian Betsch got 1,000,000,00 Mark in 1926 for his book fictions in > mathematics. Beware of saying nonsense. You will lose me because I > conclude that you are not willing to learn from me. Was that a joke? > Set > > theory says nothing of the sort. If you discuss something, you should > > have at least some knowledge of it. > > Be sure, I have, and I found set theory unfounded from the very beginning. > > > > >> From this point of view, one cannot admit that a number may be > >> void even if it turns out to be useless and maybe even misleading. > > > > More made-up words: "void", "useless", "misleading". > > My command of English does not provide more appropriate words. Let's try again: Please state one thing that you think is wrong with mathematics. Just one. And, be specific. And, concise. -- David Marcus
From: David Marcus on 9 Dec 2006 01:31 Tonico wrote: > Tony Orlow ha escrito: > > > You can call me a troll if that makes you feel better. You seem to need > > to bolster your ego by piling it on top of others. Hopefully you'll work > > that out eventually. I won't concern myself with your spiritual > > development too deeply, but I do have some questions. > > ***************************************************** > Lemme see: troll....yup, it makes me feel better....ah. If a troll has to know they are trolling, then I don't think Tony is a troll. He thinks he is merely posting what is correct. Of course, it would be better if he was a troll. He's more a crank. -- David Marcus
From: David Marcus on 9 Dec 2006 01:34 Virgil wrote: > In article <4579d1c7(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > I chose to work within computer science, after having planned to become > > a mathematician, for the obvious reasons.... > > Couldn't cut it as a mathematician? Probably couldn't understand any of his math courses. -- David Marcus
From: David Marcus on 9 Dec 2006 01:35
Tony Orlow wrote: > Okay, a "potential" infinite set is one where each element, like the > naturals, has a specific string associated with it, which has a > left-hand end. What do you mean "a specific string associated with it", and what is a "left-hand end"? -- David Marcus |