Galileo's Paradox
in [Math]
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From: Eckard Blumschein on 4 Dec 2006 11:18 On 12/1/2006 10:38 PM, Virgil wrote: > In article <45706BFD.7090506(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 11/30/2006 10:02 PM, Virgil wrote: >> >> >> I consider Dedekind wrong, and he admitted to have no evidence in order >> >> to justify his basic idea. >> > >> > The fact that Dedekind's definition of infiniteness of sets has been >> > widely adopted indicates that many others have found it to be a useful >> > definition. >> >> It was appealing even to Peirce. BTW, I referred to the lacking basis of >> his cuts. What about the definition of an infinite set, I alredy >> explained somewhere here why it tacitly implies an illusion. > > When you "explain" why 2 = 1, I am not persuaded. In this case you would probably guess that I misused division by zero. No, I did not cheat you. >> >> And utility is the measure of the value of a definition. >> >> Utility for what? > > Mathematical definitions are abbreviations, they shorten things. If they > are useful enough to be used often, they can save a great deal of time > and space in mathematical writings. They are useful for that. So you meant: Usefulness is the measure ...? I am an electrical engineer, understanding utility like a supply in particular of electric power.
From: Eckard Blumschein on 4 Dec 2006 11:34 On 12/1/2006 10:33 PM, Virgil wrote: > In article <45706AD1.808(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > You claimed many "imperfectins" but did not justify those claims with > anything mathematically valid. When I performed Fourier transform back and forth for a function stepping at t=a, cf. http://iesk.et.uni-magdeburg.de/~blumsche/M283.html I correctly returned to the original function iff I ignored the intermediate value at t=a and decided to extend integration from t<a instead. >> >> I guess, point-set topology and measure >> >> theory do not require the claim of set theory to rule all mathematics. >> > >> > They cannot exist without a foundation of set theory. >> >> In this case they could not exist. Set theory does not have a solid >> basis. So I doubt. > > There are a lot of textbooks on point-set, and other, topologies and on > measure theory. I have yet to see one of them that is not based on set > theory. If EB claims these books do not exist, he is even more foolish > than usual. I do not claim this. I just guess that not a single one really needs the transfinite numbers and nonsense cardinalities like aleph_2. >> No. Aleph_2 is just fancy. > > So EB chooses to remain ignorant in order to support his claims. Ignorant of what? Please point me to a persuading if any application of aleph_2.
From: Lester Zick on 4 Dec 2006 11:42 On Sun, 03 Dec 2006 20:24:42 -0500, Bob Kolker <nowhere(a)nowhere.com> wrote: >Lester Zick wrote: > >> On Sat, 02 Dec 2006 13:38:47 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >> >>>Lester Zick wrote: >>> >>>>On Fri, 01 Dec 2006 11:36:00 -0500, Tony Orlow <tony(a)lightlink.com> >>>>wrote: >>>> >>>> >>>>>Lester Zick wrote: >>>>> >>>>>>On Thu, 30 Nov 2006 09:52:49 +0100, Eckard Blumschein >>>>>><blumschein(a)et.uni-magdeburg.de> wrote: >>>>>> >>>>>> >>>>>>>On 11/29/2006 6:37 PM, Bob Kolker wrote: >>>>>>> >>>>>>>>Tony Orlow wrote: >>>>>>>> >>>>>>>>>It has the same cardinality perhaps, but where one set contains all the >>>>>>>>>elements of another, plus more, it can rightfully be considered a larger >>>>>>>>>set. >>>>>> >>>>>>Tony, you know we've been over this previously. All "infinite" means >>>>>>is lack of definition for a particular predicate such as numerical >>>>>>size. And when you add numerical finites to numerical infinites the >>>>>>result is still infinite. >>>>> >>>>>When you add anything to anything, you have more than you had, eh? >>>>>That's pretty basic. Let's try to keep that in mind. >>>> >>>>Provided they have the same metric and you can just "add anything to >>>>anything". Next you'll be trying to add apples and oranges. >>>> >>> >>>I can do that, by the pound, or apiece. That's a different problem. >> >> >> Oh I agree. But if you add them as pieces of fruit for example that >> requires a conversion of metrics between apples, oranges, and pieces >> of fruit or anything else they have in common according to a common >> metric. With a finite r and infinitesimal dr you don't have that >> without some common basis of metric integration. >> >> >>>>>>This problem mainly arises I suspect because mathematikers insist on >>>>>>portraying infinites as larger than naturals and somehow coming beyond >>>>>>the range of naturals such as George Gamow's famous 1, 2, 3, . . . 00. >>>>>>Then mathematkers try to establish certain numerical properties for >>>>>>infinities by comparative numerical analysis and mapping with >>>>>>numerically defined finites. However one cannot do comparative >>>>>>numerical analysis and numerical analysis with numerically undefined >>>>>>infinites anymore than one can do arithmetic. Infinites are neither >>>>>>large nor small; they're just numerically undefined. >>>>> >>>>>Uh, what if you define them, and even work out a language for expressing >>>>>them, and arithmetic that be performed on them, and they produce >>>>>intuitive results that include measure, as well as count? Why do you >>>>>claim that's impossible, because you don't like the idea? >>>> >>>>I don't like the idea because you can't establish any metric for them >>>>not because you work out all kinds of things you claim are intuitive. >>>> >>> >>>You can establish a common metric, even if you can't describe one in >>>terms of the other in a finite formula. >> >> >> Well you can say you have a common metric but that doesn't mean you >> can show one. In my opinion taking the derivative of a straight line >> such as r with respect to itself produces 0dr and shows definitively >> that there is no metric in common between r and dr. > >dr/dr = 1. So you're telling us the slope of a straight line, r, with respect to itself 1dr instead of 0 dr, Bob? Curiouser and curiouser. I don't believe anyone expressed any interest in the ratio of dr to dr but rather in the derivative of r with respect to itself. Personally I should have thought straight lines were flat. But there it is. >in general d(k*r)/dr = k, where k is a constant. Gee that's swell, Bob. Next you'll be explaining how to calculate the value of 1/1, 2/1, 3/1 . . . >> Well that seems to be pretty easy. At least taking the derivative of a >> cube like rrr with respect to r indicates a ratio of infinitesimals is >> 3rr dr for its square and with respect to r would be 6r dr. > >d(r^3)/dr = 3*r^2 Well except for the "dr" which you left off on the right hand side of the equation, I should have thought that's what I just said. >That is calculus. > >What you are babbling about is Zickulus. You have a penchant for restating the obvious and almost getting it right, Bob. Probably comes from a non linear ordering in the set of your head. ~v~~
From: Eckard Blumschein on 4 Dec 2006 11:47 On 12/1/2006 10:28 PM, Virgil wrote: > In article <457069A0.7060208(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> Cantor did know that his fancy was rejected from all important figures >> even those hundreds or even thousands of years ago. > > Is this supposed to mean something? Cantor was hospitalised in a mad house on a regular basis. He took advantage of the possibility to read and comment on work by Aristotele, Leibniz, etc. They were wrong altogether. He gave evidence for that just by claiming to be more intelligent. His style and his promise: "The essence of mathematics is just its freedom" in combination with influencial friends made him very popular. He even founded the mathematical society. During later depressive phases of his mind, he withdrew from mathematics and dealt with the putative identity of Shakespeare.
From: Lester Zick on 4 Dec 2006 12:06
On 4 Dec 2006 04:31:30 -0800, imaginatorium(a)despammed.com wrote: > >Lester Zick wrote: >> On Sat, 02 Dec 2006 13:26:13 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >Lester Zick wrote: >> >> On Fri, 01 Dec 2006 11:39:57 -0500, Tony Orlow <tony(a)lightlink.com> >> >> wrote: >> >>> Lester Zick wrote: >> >>>> On Thu, 30 Nov 2006 12:08:03 +0100, Eckard Blumschein >> >>>> <blumschein(a)et.uni-magdeburg.de> wrote: >> >>>>> On 11/29/2006 8:13 PM, Bob Kolker wrote: >> >>>>>> Tony Orlow wrote: > ><snip all that> > >> Well, Tony, I don't really think any of this matters. These just seem >> to be word strings having nothing to do with the matters at hand. > >Well, indeed. Yet curiously it manages to be entertaining from time to >time. And at least in my case more than a little true. But come now, Brian, a little question in zen math to brighten the day as Bob seems unwilling to fess up: in modern math does set "theory" represent all of mathematics as Bob seems to think and does it have a pre emptive prerogative with respect to the definition of terms like "cardinality" and so on in mathematics? I'm inclined to consider that set "theory" is really only a parochial group of analytical techniques which are inexhaustive at best and problematic in any event and not really a theory at all. ~v~~ |