Cantor Confusion
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From: imaginatorium on 31 Oct 2006 01:21 MoeBlee 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. 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. > > 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'. 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? Gosh, are you asking Lester this? Looks like another definition of "optimist" for my collection... Brian Chandler http://imaginatorium.org (Yeah, I look both ways before crossing a one-way street, particularly around here)
From: imaginatorium on 31 Oct 2006 01:32 David Marcus wrote: > Lester Zick wrote: > > On Mon, 30 Oct 2006 16:43:03 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > >Han de Bruijn wrote: > > >> David Marcus wrote: > > >> > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > >> >>And add this to the fact that noon and beyond cannot exist > > >> >>in this problem. > > >> > > > >> > Are you still doing physics, water, and a finite number of molecules? > > >> > Let us know when you switch to mathematics. > > >> > > >> I'm DOING mathematics. Mathematics is NOT independent of Physics. > > > > > >I guess your definition of "mathematics" is different from mine. > > > > I think the only relevant question is whether your definition of > > "mathematics" is demonstrably true? If not I don't see that any > > definition of mathematics is more virtuous one way or the other. > > That would depend on what your definition of "demonstrably true" is. My > definition of "mathematics" agrees with what mathematicians do. > > Is it "demonstrably true" that "noon... cannot exist"? Be careful not to mix up your interlocutors - this is Lester, and I expect he will only be interested in whether noon is true or not. Brian Chandler http://imaginatorium.org
From: David Marcus on 31 Oct 2006 02:16 imaginatorium(a)despammed.com wrote: > David Marcus wrote: > > Lester Zick wrote: > > > On Mon, 30 Oct 2006 16:43:03 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > > >Han de Bruijn wrote: > > > >> David Marcus wrote: > > > >> > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > > > >> >>And add this to the fact that noon and beyond cannot exist > > > >> >>in this problem. > > > >> > > > > >> > Are you still doing physics, water, and a finite number of molecules? > > > >> > Let us know when you switch to mathematics. > > > >> > > > >> I'm DOING mathematics. Mathematics is NOT independent of Physics. > > > > > > > >I guess your definition of "mathematics" is different from mine. > > > > > > I think the only relevant question is whether your definition of > > > "mathematics" is demonstrably true? If not I don't see that any > > > definition of mathematics is more virtuous one way or the other. > > > > That would depend on what your definition of "demonstrably true" is. My > > definition of "mathematics" agrees with what mathematicians do. > > > > Is it "demonstrably true" that "noon... cannot exist"? > > Be careful not to mix up your interlocutors - this is Lester, and I > expect he will only be interested in whether noon is true or not. I think I realized that Lester was commenting on something I said to Han, and I was asking Lester (just out of idle curiosity) if he thought that Han's idea of "mathematics" satisfied Lester's criterion. I wonder: do Lester, Ross, Han, Tony, and WM all agree that noon doesn't exist? It is such an odd thing to say. Imagine walking up to someone in the street and trying to convince them that noon doesn't exist. It is so hard to keep the nonsense straight. It all seems to run together--although there are stylistic differences. An insistence that words mean whatever the writer wants them to mean (if they mean anything at all) seems to underly most of the poetry. -- David Marcus
From: Han de Bruijn on 31 Oct 2006 03:41 stephen(a)nomail.com wrote: > Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > >>stephen(a)nomail.com wrote: > >>>Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >>> >>>>I'm DOING mathematics. Mathematics is NOT independent of Physics. >>> >>>5*10^8 m/s + 5*10^8 m/s = 10*10^8 m/s > >>There are 10 men in a room. Each has a body temperature of 37 Celcius. >>This means that the temperature in the room is: 10 x 37 = 370 Celcius. >>Satisfied? Or do you rather prefer it in Kelvin? > > Satisfied? I have no idea what you mean. Either you are agreeing with > me or you totally missed my point. [ ... snip ... ] Who is missing who's point? Han de Bruijn
From: Albrecht on 31 Oct 2006 03:52
Sebastian Holzmann schrieb: > mueckenh(a)rz.fh-augsburg.de <mueckenh(a)rz.fh-augsburg.de> wrote: > > "dirty" is a property which without the axiom of dirt is as well > > defined as "infinite" without the axiom of infinity. > > No. A set x (which is here to denote an element of a model M of ZF-INF) > is called "finite" if x satisfies one of the following conditions: > > 0: x does not have an element > 1: x has exactly one element > 2: x has exactly two elements > and so on > > otherwise, x is called "infinite". Where do I need the axiom of infinity > to do this? Since there is no x which don't follow one of your conditions 0, 1, 2, .... you may call the otherwise x as you want. You can call them "muggles" without an axiom of muggles if you want. Best regards Albrecht S. Storz |