Cantor Confusion
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From: David Marcus on 31 Oct 2006 18:52 Virgil wrote: > In article <bdc92$45476e9e$82a1e228$30478(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > It's easy to come up with a correct physical problem and > > solve it with the wrong mathematics. As you did. > > HdB has come up with a mathematical problem which he claims can end the > world: > > HdB claimed that a discontinuity in a mathematical function of time > causes time to stop. And he claimed this followed from physics. > > Thus, if HdB is right, the vase problem will cause the end of the > world. Yes, but when? -- David Marcus
From: David Marcus on 31 Oct 2006 18:54 Han de Bruijn wrote: > David Marcus wrote: > > > I guess your definition of "mathematics" is different from mine. > > Yes. Like your definition of "physics" is different from mine. I certainly hope so. -- David Marcus
From: MoeBlee on 31 Oct 2006 18:57 Lester Zick wrote: > On 30 Oct 2006 15:30:42 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > > >Lester Zick wrote: > >> On 30 Oct 2006 12:12:00 -0800, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > >> > >> >mueckenh(a)rz.fh-augsburg.de wrote: > >> >> Get it right: It is nonsense to talk about infinite sets if there is no > >> >> axiom of infinity and, therefore, no possible definition of infinity. > >> > > >> >No, YOU need to get it right. You have it completely wrong. We don't > >> >need the axiom of infinity to define the predicate 'is infinite'. > >> > >> But you certainly need something you ain't got besides the adjective > >> "infinite" to define the predicate "infinity". > > > >I never proposed considering 'infinity' as a predicate nor defining > >'infinity' as a predicate or a noun. > > Obviously since you can't do it. I don't need to do it, since the formal theories I study do not have 'infinity' as locutions in the theory. > > > So since the other poster > >mentioned the impossibility of defining 'infinity', your point is well > >taken if it is that I should be clear that I am not responding to the > >poster's exact point about 'infinity' but rather that I am commenting > >upon the fact that we do have definitions of 'is infinite' without > >having to adopt the axiom of infinity. > > I have no idea what the axiom of infinity may be and don't especially > care since all mathematikers want to talk about is infinite(x) and not > infinity. > > >This boils down to the fact that set theory defiines 'is infinite' but > >there need not be any pretension on the part of set theory to define > >'infinity'. > > Pretension??? See, Moe, we're right back to the same old bullshit. > Modern mathematikers want to use the idea of "infinity" If I ever use the word 'infinity' to render any of the formal mathematics I study, then I'll define 'infinity'. > without having > to define it by referring to the "infinity of x" instead. No, not 'infinity of x', but rather 'x is infinite', as I wrote. > Fact is that > modern mathematikers want to have their cake and eat it too. They use > the terms "truth" and "infinity" all the time but when they're called > on it they pretend they're using "truth(x)" and "infinite(x)" instead. > That's what I call pretentious. Since you know nothing about the mathematics you're talking about, I don't care what you consider pretentious. > > What the theory NEEDS in order to do the math that it > >expresses is to define 'is infnite'; while it is not needed to define > >'infinity'. Whatever need there is to define 'infinity' is a need that > >is extra to the usual mathematical purposes of devising a set theory > >and definitions in it. > > > >Do you see what am saying? > > Yeah, Moe, I see exactly what you're saying. You're saying that if you > get enough particular definitions of "infinite(x)" and "true(x)" you > might someday wind up with some idea what "infinity" and "truth" are. Nope. Not what I'm saying. MoeBlee
From: David Marcus on 31 Oct 2006 18:58 mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > > The set of natural numbers is an infinite set that contains only finite > > numbers. > > Please do not assert over and over again this unsubstantiated nonsense > (this word means exactly what you think) but give an example, please, > of a natural number which does not belong to a finite sequence. If you > cannot do so, then it is obviously unnecessary to consider N as an > infinite sequence, because all its members belong to finite sequences. I didn't say anything about sequences, finite or otherwise. So, your request is irrelevant to my statement. Are you using standard terminology and standard axioms (ZFC) or are you off in your own world again? -- David Marcus
From: David Marcus on 31 Oct 2006 19:00
mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > > > Do and enjoy your mathematics. I will not disturb you. > > > > Then why are you posting to sci.math? What do you possibly hope to > > achieve? > > To help those who have not yet decided to study set theory to avoid > wasting their time. But, since you clearly haven't studied set theory, how do you know it is a waste of time? -- David Marcus |