Cantor Confusion
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From: Lester Zick on 25 Oct 2006 14:23 On Wed, 25 Oct 2006 11:45:04 +0000 (UTC), stephen(a)nomail.com wrote: >David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> Lester Zick wrote: >>> >> In article <1161377915.999210.39660(a)m7g2000cwm.googlegroups.com> "MoeBlee" <jazzmobe(a)hotmail.com> writes: >>> >> > mueck...(a)rz.fh-augsburg.de wrote: >>> >> ... >>> >> > Okay, now that I asked for a definition of the relation you mentioned, >>> >> > you're not giving that definition, but instead giving a >>> >> > combinatorical/numerical argument with more terminology. What is a >>> >> > "load of edges"? What is the definition of "a path carries a load of >>> >> > edges"? If this is standard terminology in graph theory, then please >>> >> > forgive my ignorance and supply me with the standard definition. If it >>> >> > is not standard terminology, then please give me your own definition. >>> >> >>> >> By this time you ought to know that Mueckenheim *never* gives definitions. >>> >> Or actually states that he is not able to give a definition for a >>> >> particular term. Asking for definitions from Mueckenheim is as useful as >>> >> talking to an eel. >>> > >>> >This does seem to be true. I suspect he doesn't know what the word >>> >"definition" means in mathematics. >>> >>> "Definition" in mathematics would appear to mean pretty much whatever >>> people who claim to do mathematics say it means. Ex: Cardinality is >>> card(x)= least ordinal(x) equinumerous(x). In other words mathematical >>> definition is when definition(x) defines mathematical definition(x).Or >>> mathematics is when mathematician(x) and a mathematician is when >>> mathematics(x). I don't know whether M. gives mathematical definitions >>> or not.However I know a great many mathematikers who definitely don't. > >> OK, so both Mueckenheim and you don't know what the word "definition" >> means in Mathematics. I suppose most of us already knew that. What we >> find somewhat puzzling is why you don't take the trouble to learn. Have >> you tried, but not been able to? What math courses have you taken? > >> -- >> David Marcus > >You are talking to someone who thinks that dr/dt = r/t for >circular motion, where r is the radius and t is time. Do >not expect anything sensible. Or talk to Stephen if you'd prefer someone who thinks dr is velocity. ~v~~
From: Lester Zick on 25 Oct 2006 14:25 On Tue, 24 Oct 2006 17:34:46 -0600, Virgil <virgil(a)comcast.net> wrote: > >> In article <1161683860.442902.89560(a)b28g2000cwb.googlegroups.com> >> mueckenh(a)rz.fh-augsburg.de writes: > >> > If f(0) is undefined, i.e., if 0 is not element of the domain of f, >> > then we can find f(0) = 0 by l'Hospital' s rule. Ever heard of? > > >L'Hopital's rule has very restricted application in the finding of >limits, and is in no way applicable in anything cited here. > >L'Hopital's rule is also often a refuge of the mathematically >incompetent in many of the rare cases where it is applicable. Whereas the spelling of L'Hospital's rule is also often a refuge of verbal incompetents. ~v~~
From: David Marcus on 25 Oct 2006 14:33 stephen(a)nomail.com wrote: > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > Lester Zick wrote: > >> "Definition" in mathematics would appear to mean pretty much whatever > >> people who claim to do mathematics say it means. Ex: Cardinality is > >> card(x)= least ordinal(x) equinumerous(x). In other words mathematical > >> definition is when definition(x) defines mathematical definition(x).Or > >> mathematics is when mathematician(x) and a mathematician is when > >> mathematics(x). I don't know whether M. gives mathematical definitions > >> or not.However I know a great many mathematikers who definitely don't. > > > OK, so both Mueckenheim and you don't know what the word "definition" > > means in Mathematics. I suppose most of us already knew that. What we > > find somewhat puzzling is why you don't take the trouble to learn. Have > > you tried, but not been able to? What math courses have you taken? > > You are talking to someone who thinks that dr/dt = r/t for > circular motion, where r is the radius and t is time. Do > not expect anything sensible. Don't worry: My expectations are very low. -- David Marcus
From: Lester Zick on 25 Oct 2006 15:37 On Wed, 25 Oct 2006 00:47:27 -0400, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Lester Zick wrote: >> On Mon, 23 Oct 2006 22:16:36 -0400, David Marcus >> <DavidMarcus(a)alumdotmit.edu> wrote: >> >Dik T. Winter wrote: >> >> In article <1161377915.999210.39660(a)m7g2000cwm.googlegroups.com> "MoeBlee" <jazzmobe(a)hotmail.com> writes: >> >> > mueck...(a)rz.fh-augsburg.de wrote: >> >> ... >> >> > Okay, now that I asked for a definition of the relation you mentioned, >> >> > you're not giving that definition, but instead giving a >> >> > combinatorical/numerical argument with more terminology. What is a >> >> > "load of edges"? What is the definition of "a path carries a load of >> >> > edges"? If this is standard terminology in graph theory, then please >> >> > forgive my ignorance and supply me with the standard definition. If it >> >> > is not standard terminology, then please give me your own definition. >> >> >> >> By this time you ought to know that Mueckenheim *never* gives definitions. >> >> Or actually states that he is not able to give a definition for a >> >> particular term. Asking for definitions from Mueckenheim is as useful as >> >> talking to an eel. >> > >> >This does seem to be true. I suspect he doesn't know what the word >> >"definition" means in mathematics. >> >> "Definition" in mathematics would appear to mean pretty much whatever >> people who claim to do mathematics say it means. Ex: Cardinality is >> card(x)= least ordinal(x) equinumerous(x). In other words mathematical >> definition is when definition(x) defines mathematical definition(x).Or >> mathematics is when mathematician(x) and a mathematician is when >> mathematics(x). I don't know whether M. gives mathematical definitions >> or not.However I know a great many mathematikers who definitely don't. > >OK, so both Mueckenheim and you don't know what the word "definition" >means in Mathematics. I suppose most of us already knew that. What we >find somewhat puzzling is why you don't take the trouble to learn. My general policy is that if I can't learn a doctrine second hand from advocates who claimed to have learned it first hand I have no desire to become a member of their well ordered, robust, non bijective set. > Have >you tried, but not been able to? What math courses have you taken? OK. So let's try a mathematical definition of crankiness on for size. Crank(x)=disagree(u). ~v~~
From: mueckenh on 25 Oct 2006 15:53
Sebastian Holzmann schrieb: > mueckenh(a)rz.fh-augsburg.de <mueckenh(a)rz.fh-augsburg.de> wrote: > > > > Sebastian Holzmann schrieb: > >> Let's assume that ZFC - AoI is consistent, otherwise the statement is > >> void. Let \phi_n be a sentence in the language of set theory that > >> encodes the statement "There exists a set that has at least n elements" > >> (you can formulate this one as a homework problem). > > > > Perhaps you do another homework first: Why should such such a sentence > > be correct? It is not difficult to encode the sentence: Card(Q) > > > Card(R). Is that a proof? > > Such a sentence should not be "correct". It cannot be ecxcluded without the axiom of infinity. Because you cannot even talk about these sets. >Perhaps you should think of it > as a request for a certain property. Can you formulate it in the > language of set theory? It is a good exercise when you want to take part > in discussions about mathematical logic. Oh no, not that! It is enough to know that the subject of what you call "logic" is nonsense. > > Of course a sentence "Card(Q) > Card(R)" is not a proof. Please consult > a book on mathematical logic, set theory and model theory. > > >> Since for every finite subset of the set of \phi_n, there exists a model > >> of ZFC - AoI where this subset is true (any model of ZFC - AoI should do > >> the trick), by compactness, there exists a model of ZFC - AoI where > >> _all_ \phi_n are simultaneously true. ("True" might not be the correct > >> English word for it, please do someone correct me in this.) A set that > >> has, for any n, at least n elements cannot be finite. Therefore it must > >> be infinite. > > > > Further in this case it would be nonsense to introduce the axiom of > > infinity. > > The axiom of infinity is added in ZFC to ensure that an infinite set > exists in _any_ model of the theory. I am afraid, it will be useless for you to consult any books. Nevertheless, here is my attempt to teach you some real logic: Vor allem ist die Bildung der wichtigsten Klasse paradoxer Mengen, nämlich der allzu umfassenden Mengen (Antinomien von Burali-Forti, Russell usw.) durch unsere Axiome ausgeschlossen. Denn diese gestatten, eine oder mehrere gegebene Mengen als Ausgangspunkt nehmend, nur entweder die Bildung beschränkterer Mengen durch Aussonderung bzw. Auswahl, oder die Bildung von Mengen, die in eng umschriebenem Maß sozusagen umfassender sind, durch Paarung, Vereinigung, Potenzierung usw. Regards, WM |