Cantor Confusion
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From: Lester Zick on 27 Oct 2006 15:25 On Fri, 27 Oct 2006 00:36:24 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote: [. . .] >You need transfinity when you want to show that something that holds in >the finite case also is valid in the infinite case. Induction will not >show that 0.111... is rational, it can only show that all the finite >initial parts are rational. And I again note that the notation 0.111... >(in the decimals) has only meaning due to the definition of that notation. However one can certainly show the square root of 2 without transfinity through rac construction even though its decimal expansion is infinite. ~v~~
From: Virgil on 27 Oct 2006 15:53 In article <7df55$4541bb03$82a1e228$27136(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <1161884380.178413.126960(a)i3g2000cwc.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > > >>David Marcus schrieb: > >> > >>>>All the balls have been removed before noon. > >>> > >>>OK. > >>> > >>>>But more balls are in the vase. > >>> > >>>Reason? Proof? Example? Anything? > >> > >>Consider a strictly increasing sequence with non-negative > >>terms.--------- If you can. > > > > Consider that the number of balls as a function of time has infinitely > > many integer jump discontinuities which cluster around noon, so that > > there is no way that the function can be continuous at noon. > > Huh! Consider the Ocean as defined by Tony Orlow. Replace the balls in a > vase by the water molecules in an ocean - what hell is the difference!? > Then use a continuous model, as is _routinely done_ with Fluid Dynamics. > And there IS a way that the function can be continuous at noon. But the > problem is that you mathematicians do not understand what continuity IS. > You cannot comprehend that there can be a discrete as well as continuous > description for one and the same (physical) phenomenon. See for example > the Fluid Tube Continuum: > > http://hdebruijn.soo.dto.tudelft.nl/QED/index.htm#ft > > Han de Bruijn Does HdB claim that the vase problem can be run in the physical world? "What the Hell is the difference" is that in mathematical worlds things do not always conform to the demands of physicists. Does HdB dispute that, according to the Gedankenexperiment as originally stated that, every ball inserted before noon is also removed before noon?
From: MoeBlee on 27 Oct 2006 16:05 David Marcus wrote: > Not sure if he ever said precisely "within Z set theory", but he > certainly said things very similar. Below are a few messages that I > found. There are probably others. > > In the first, he says that "standard mathematics contains a > contradiction". In the next two, he states there are "internal > contradictions of set theory". In the next, I say that he says that > "standard mathematics contains a contradiction", and he does not > dispute this. Thanks. And at least a couple of times I said that I was reading his argument to see whether it does sustain his claim about set theory, as I mentioned specifically Z set theory. How rude. He tells you he's going to demonstrate something "IN" set theory, so, ON THAT BASIS, you take the time to ponder his argument, then he just pulls the rug out from under by saying that it's something "outside" of ZFC but that "covers" ZFC. MoeBlee
From: David Marcus on 27 Oct 2006 16:17 MoeBlee wrote: > David Marcus wrote: > > Not sure if he ever said precisely "within Z set theory", but he > > certainly said things very similar. Below are a few messages that I > > found. There are probably others. > > > > In the first, he says that "standard mathematics contains a > > contradiction". In the next two, he states there are "internal > > contradictions of set theory". In the next, I say that he says that > > "standard mathematics contains a contradiction", and he does not > > dispute this. > > Thanks. And at least a couple of times I said that I was reading his > argument to see whether it does sustain his claim about set theory, as > I mentioned specifically Z set theory. > > How rude. He tells you he's going to demonstrate something "IN" set > theory, so, ON THAT BASIS, you take the time to ponder his argument, > then he just pulls the rug out from under by saying that it's something > "outside" of ZFC but that "covers" ZFC. I seriously doubt he understands the difference. He doesn't seem to really understand that modern mathematics rests on an axiomatic foundation. And, that there are certain agreed upon rules of argument (codified in the axioms) that people use. If someone wants to use some other rule of argument, they should clearly state that they are doing so. This is just a common sense prerequisite for communication. -- David Marcus
From: MoeBlee on 27 Oct 2006 19:56
Lester Zick wrote: > >> You mean that mathematical definitions can't have different "domains > >> of discourse" and mathematical definitions in different domains of > >> discourse can't borrow from one another? > > > >No, that's not what I said. > > Then why exactly are you complaining about what I said? Frankly, Moe, > you don't seem to have said much of anything that I can make out. If > mathematical definitions can have different domains of discourse then > what I wrote should be perfectly acceptable according to your own > definition of mathematical definitions and domains of discourse.. Since I never said anything that can be paraphrased as the jumble of nonsense you just mentioned, nothing I did write entails that the jumble of nonsense you wrote needs to be acceptable to me. > >No, you posted utter nonsense ("Cardinality(x)=least ordinal(y) with > >equinumerosity(z)") as if it is something that I had said. > > I never said you had said that. You're absurd. You quoted me asking you what I said that justified a certain statement you made. You directly replied to that quote with "Cardinality(x)=least ordinal(y) with > >equinumerosity(z)". > Says who exactly, Moe? Who died and made you arbiter of the universe? Apparently a rival of the authority that died and made you the arbiter as to what is "perfectly acceptable forensic modality". MoeBlee P.S. My doubleposts and duplicate passages (from posts I thought were not previously accepted by the interface) are unintentional. |