Cantor Confusion
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From: Virgil on 6 Feb 2007 15:35 In article <1170758154.230154.55880(a)m58g2000cwm.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > On 6 Feb., 11:22, Franziska Neugebauer <Franziska- > Neugeba...(a)neugeb.dnsalias.net> wrote: > > mueck...(a)rz.fh-augsburg.de wrote: > > > Franziska Neugebauer wrote: > > [...] > > >> > The simplest reason is that omega - n = omega for all n in N. > > > > >> Where did you get that from? Reference? EB? > > > > > You could even figure it out by yourself. > > > > I cannot find any reference. Perhaps, there is none. > > > > F. N. > > -- > > xyz > > Already Cantor knew it, but I am too lazy to look for the reference. > Read his papers, then you will encounter it. > > Regards, WM It is, in any case, irrelevant as a justification for what WM claimed.
From: G. Frege on 6 Feb 2007 15:56 On Tue, 06 Feb 2007 13:31:17 -0700, Virgil <virgil(a)comcast.net> wrote: > > WM seems to be unable to understand anything having to do with > mathematics or logic, therefore he should stop here. > This is rather old news... "Learn some logic. Learn some mathematics. Or better yet, give up mathematics and take up basket weaving. " (Bob Kolker, sci. math, 5 Jun. 2005) F. -- E-mail: info<at>simple-line<dot>de
From: cbrown on 6 Feb 2007 16:30 On Feb 6, 3:27 am, mueck...(a)rz.fh-augsburg.de wrote: > On 5 Feb., 05:10, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > > > > What *is* IIII. You never have defined it. You really do not like > > definitions, as they pin down the real meaning. > > IIII is a primitive. Everybody knows it - even without definition by > Peano or Dedekind. That means, we do not need Peano to know small > natural numbers. > > > > > > Henry VIII had 7 predecessors --- only including him they were 8 > > > Henries. > > > You are shifting position again? > > No. I could use IIIIIII but I can use abbreviations like VII or 7. > > > When I asked you about what basic > > way, III c IV c V, you answered that I had to continue with IIII, > > IIIII, etc. > > The basic way to establish IV c V is to use the numbers in their basic > form IIII c IIIII. (Numbers *are* their representations.) > > > > > > > > Correct, for instance for 1/7. > > > > > And for computable numbers some representation does exist. > > > > But this representation does not necessarily enable us to determine > > > the trichotomy relation with numbers which are really numbers. > > > Perhaps. How do you establish trichotomy between 1/13 and 1/64? > > Are you really going to base-26 to establish that? That would be > > pathetic. > > But it would be possible! It would yield the famous "mathematical > precision" if this could not be establised otherwise. > Do you now return to your claim that there exists a surjection from 1/13 onto 1/64, but not from 1/64 onto 1/13? Cheers - Chas
From: Virgil on 6 Feb 2007 17:07 In article <1170761231.100893.322920(a)v33g2000cwv.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > On 5 Feb., 05:10, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > > > > What *is* IIII. You never have defined it. You really do not like > > definitions, as they pin down the real meaning. > > IIII is a primitive. Everybody knows it - even without definition by > Peano or Dedekind. That means, we do not need Peano to know small > natural numbers. It is what "everybody knows" but which nobody bothers to make clear that is the basis for much confusion and disagreement. > > > > > Henry VIII had 7 predecessors --- only including him they were 8 > > > Henries. > > > > You are shifting position again? > > No. I could use IIIIIII but I can use abbreviations like VII or 7. > > > When I asked you about what basic > > way, III c IV c V, you answered that I had to continue with IIII, > > IIIII, etc. > > > The basic way to establish IV c V is to use the numbers in their basic > form IIII c IIIII. (Numbers *are* their representations.) Numerals are no more numbers than names are people. > > > > > > > Correct, for instance for 1/7. > > > > > > > > And for computable numbers some representation does exist. > > > > > > But this representation does not necessarily enable us to determine > > > the trichotomy relation with numbers which are really numbers. > > > > Perhaps. How do you establish trichotomy between 1/13 and 1/64? > > Are you really going to base-26 to establish that? That would be > > pathetic. > > But it would be possible! It would yield the famous "mathematical > precision" if this could not be establised otherwise. > > > > > > > > > 1) 1 ist eine nat�rliche Zahl. > > > > > > > 2) Jede Zahl a in N hat einen bestimmten Nachfolger a' in N. > > ... > > > > This is a recursive definition of natural numbers. By (1) we have one > > > > natural number, by (2), from that single natural number we get a lot > > > > of > > > > other natural numbers. > > > > > > Why do you say N is wrong in (2) but not in (1)? > > > > Where in (1) is N? I do not see N at all. > > "1 ist eine nat�rliche Zahl "means "1 in N". The property "being a > natural number" implies the existence of N. Of course the requirement > to decide whether n is in N is more circular than the statement that 1 > is in N. > > > > > > This is getting phylosofical. In mathematics a definition is circular > > > > if > > > > in the definition one of the deciding features is the term you want to > > > > define. So a definition as you gave: > > > > 3 is the set of all sets of 3 elements > > > > is a perfect example of a circular definition. > > > > > > !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IT IS NOT A > > > DEFINITION !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! > > > > You stated that when I asked you for a definition. So what is happening > > here? > > You will have read the definitions in my book. "3 is the set of all > sets of 3 elements" is explained in chapter 10. Why should anyone read a book on mathematics by someone who daily dispalys his incompetence at the subject. > > There is something called reality and another thing called matheology. > Both are disjoint. Since mathEology is purely the creation of WM, let is by all means avoid it and get back to the reality of actual mathematics, and henceforth eschew WM'S mathEology.
From: G. Frege on 6 Feb 2007 17:21
On Tue, 06 Feb 2007 15:07:21 -0700, Virgil <virgil(a)comcast.net> wrote: >> >> Numbers *are* their representations. [WM] >> > Numerals are no more numbers than names are people. > It seems that this is a common "theme" among cranks: they constantly mis-take the name with the object denoted by the name. "In the sentence the name represents the object. Objects I can only /name/. Signs represent them. I can only speak /of/ them. I cannot /assert them/. [...]" (Ludwig Wittgenstein, TLP, 3.22 & 3.221) F. -- E-mail: info<at>simple-line<dot>de |