Cantor Confusion
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From: Lester Zick on 20 Nov 2006 14:13 On Sun, 19 Nov 2006 18:17:31 -0700, Virgil <virgil(a)comcast.net> wrote: >In article <MPG.1fcaa991fbcf433d989963(a)news.rcn.com>, > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > >> Lester Zick wrote: >> > On Sat, 18 Nov 2006 13:31:27 -0500, David Marcus >> > <DavidMarcus(a)alumdotmit.edu> wrote: >> > >Lester Zick wrote: >> > >> On Thu, 16 Nov 2006 02:28:14 -0500, David Marcus >> > >> <DavidMarcus(a)alumdotmit.edu> wrote: >> > > >> > >> > Are you saying you don't know what the word "proof" means in >> > >> > mathematics? >> > >> >> > >> I'm saying you can't prove the truth of whatever you say in or about >> > >> mathematics. >> > > >> > >But, do you know what the word "prove" means in Mathematics? It isn't >> > >the same as what it means in English. >> > >> > Hey gimme a break. I'm still trying to biject the set of {proven} with >> > the set of {true}. Not happening. >> >> I suppose that means you don't know what the word "prove" means in >> mathematics. I suggest you refrain from responding to any posts that >> contain the word. >> >> > >> >Have you read any math books at the junior/senior college level or >> > >> >above? >> > >> >> > >> Apparently more than you. >> > > >> > >Could be. Which math books have you read? >> > >> > None. >> > >> > >> >What books on the topic have you read? What courses have you taken? >> > >> >> > >> Apparently more than you. >> > > >> > >Could be. Which books have you read and which courses have you taken? >> > >> > None. >> >> Ignorance is bliss? >> >> I'm not sure how you could have read more books than me if you've read >> none. > >Doesn't such a concatenation of claims, having read more books that you >and having read none, qualify Zick for a stupid award? It certainly qualifies you for one. ~v~~
From: Franziska Neugebauer on 20 Nov 2006 14:22 David Marcus wrote: > mueckenh(a)rz.fh-augsburg.de wrote: [...] >> You wrote: "The cardinality of omega is |omega| not omega." >> >> Shall this sentence of yours express a difference between |omega| >> and omega or not? (Now I recognize why it is so difficult to convince >> the proponents sof set theory.) > > Franziska explained that what [s]he meant was that the notation for > the "cardinality of omega" is "|omega|", not "omega". It turns out > (using a standard definition for cardinality) that |omega| = omega. Thanks for the confirmation of understandability. F. N. -- xyz
From: David Marcus on 20 Nov 2006 14:28 stephen(a)nomail.com wrote: > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > mueckenh(a)rz.fh-augsburg.de wrote: > > >> No. A well-order of the real numbers is not definable. A well-order of > >> the real numbers cannot be given by a list. There is no other means > >> which could well-order the real numbers. To believe that it exists > >> (where should it exist?) is a certificate of distinguished madness at > >> an advanced level. > > > Why do things that "exist" have to exist "somewhere"? Where does the > > number five exist? > > Right next to the number four? :) Oh, right. I knew I left it somewhere around here... -- David Marcus
From: David Marcus on 20 Nov 2006 14:35 Lester Zick wrote: > On Sun, 19 Nov 2006 17:53:12 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > >Lester Zick wrote: > >> On Sat, 18 Nov 2006 13:44:58 -0500, David Marcus > >> <DavidMarcus(a)alumdotmit.edu> wrote: > >> >Lester Zick wrote: > > > >> >> I'm saying that you don't understand what a mathematical definition is > >> >> but nonetheless want to pretend you do. If a mathematical definition > >> >> were "just" an abbreviation as you claim you wouldn't have any way to > >> >> tell one mathematical definition from another. > >> > > >> >Why not? Suppose I make the following definitions. > >> > > >> > Let N denote the set of natural numbers. > >> > Let R denote the set of real numbers. > >> > > >> >Then I can tell N and R are different because their defintions are > >> >different. If I write > >> > > >> > 0.5 is not in N, > >> > > >> >then this means the same as > >> > > >> > 0.5 is not in the set of natural numbers. > >> > > >> >And, it means something different from > >> > > >> > 0.5 is not in R. > >> > >> But the problem, sport, is you claim mathematical definitions are > >> "only abbreviations". Granted I suppose even mathematikers can tell > >> the difference between N and R in typographical terms. I mean they may > >> be too lazy and stupid to demonstrate the truth of what they say but > >> even they can see differences in typography. But in terms of > >> abbreviations alone we can't really say what the difference is between > >> N and R because you insist their definitions are "only abbreviations" > >> and not their conceptual content. > > > >You said there was no way to tell two definitions apart. The > >typographical difference suffices to tell the definitions apart (as you > >just admitted). > > So what exactly is the difference between definitions N and R in > conceptual terms if definitions are "only abbreviations"? I mean you > say certain things about definitions which are mutually inconsistent. > If definitions were "only abbreviations" as you indicate then your > definitions for N and R would be restricted to those abbreviations N > and R. Instead you append certain properties to each and pretend that > they're part of the definitions for N and R which we'll all can see > are not part of their abbreviations such that your definition for > definitions is "only abbreviations which are not only abbreviations". > Obviously this kind of logic extends way beyond your doctoral thesis > in philosophy but is nonetheless true. That's impressive. Either you are trolling or you have completely misunderstood what people mean when they say "definitions are abbreviations". -- David Marcus
From: David Marcus on 20 Nov 2006 14:37
Franziska Neugebauer wrote: > David Marcus wrote: > > > mueckenh(a)rz.fh-augsburg.de wrote: > [...] > >> You wrote: "The cardinality of omega is |omega| not omega." > >> > >> Shall this sentence of yours express a difference between |omega| > >> and omega or not? (Now I recognize why it is so difficult to convince > >> the proponents sof set theory.) > > > > Franziska explained that what [s]he Oops. Very sorry. > > meant was that the notation for > > the "cardinality of omega" is "|omega|", not "omega". It turns out > > (using a standard definition for cardinality) that |omega| = omega. > > Thanks for the confirmation of understandability. You're welcome. -- David Marcus |