
Re: Peerreviewed arguments against Cantor Diagonalization
Posted:
Oct 30, 2012 2:09 AM


LudovicoVan wrote:
> "Peter Webb" <webbfamilyDIEspamDie@optusnet.com.au> wrote in message > news:k6nk8v$lht$1@news.albasani.net... > > LudovicoVan wrote: > >>"Peter Webb" <webbfamilyDIEspamDie@optusnet.com.au> wrote in message > > > news:k6nfnq$dre$1@news.albasani.net... > >>> LudovicoVan wrote: > >>>>"Peter Webb" <webbfamilyDIEspamDie@optusnet.com.au> wrote in > message >>> > news:k6l6as$h0q$1@news.albasani.net... > >>> > > >>>>> As you haven't told us what "w" and "m" are supposed to be, or > the >>>>> rule that you are using to form the list, this cannot be > done. >>> > > >>> > Parrot, at least read bloody Cantor's argument before > >>> > pontificating your dogma. > > > > > >>> I have. And its not dogma. > > > > > > But you have just asked what "w" and "m" are supposed to mean, > > > remember? That's why I call you (and co., don't take it > > > personally as it isn't) parrots etc.: because you are just right, > > > whatever kind of bollocks you might say, in the end you are still > > > right. By dogma, and the guns. > > > > You actually have to identify what I said which you think is > > "bollocks". > > > > Somehow you forgot to say what it is. > > I have just said it... Unless you mean a full list of all the > bollocks ever stated in sci.math: of course, just forget it.
No, I want to know what I said which you think is "bollocks".
Why won't you tell us?
> > >>>>> If you think you have a list of all Reals, post it here, and I > >>will >>> happily prove its not a list of all Reals by finding a Real > >>not on >>> the list for you. > >>> > > >>> > But you can do no such thing: the antidiagonal is just not a > real >>> > number. > > > > > >>> Of course it is a Real number. It is the limit of a Cauchy > sequence. >>> You do know that convergent Cauchy sequences define > unique Reals, >>> right? > > > > > >>> (I just bagged somebody for providing a proof of the antidiagonal > >>> was Real using Cauchy sequences, on the basis that no crank > disputes >>> whether the antidiagonal is Real. And then you prove me > wrong by >>> raising exactly this isuue). > > > > > > Indeed, to be precise, you and co. excel in not even being wrong. > > > > >>> So, where is your list of all the Reals? > > > > > > The real numbers are a subset of the surreals. But I had said > > > that already. Of course they are countable: > > > > Terrific. Provide a surjection from N to R. > > Ever heard of the surreals at all?
Of course. But we are discussing Reals, not Surreals.
> But you are correct in that I was > imprecise: all infinite sets are *extendedcountable*, i.e. all > infinite sets biject with N*, the extended naturals.
The "extended Naturals, huh"? Do you mean the naturals extended with transfinite elements represented with "nonstandard numbers", as for example in http://en.wikipedia.org/wiki/Nonstandard_model_of_arithmetic ?
If so, your comment is meaningless, as these theories only add a countably infinite number of new "numbers", so the cardinality of N extended in this manner is identical to the cardinality of N alone.
If you mean something else by the "extended naturals", you should tell us what it is.
> > >> there just is no such thing as > > > a number that is not a number: a number is all we can do with it > > > seriously (you won't get this, but never mind). > > > > You are supposed to either say what you think I said which is > > bollocks, or provide a counterexample to Cantor. > > > > As it is, you are just mumbling. > > > > > Well, maybe it's not dogma, it's just that you cannot read... But > > > no, I am not optimistic about anybody's intellectual honesty > > > around here: except maybe for Prof. Magidin, who at least shows > > > some good math. > > > > The cranks should be pretty obvious. Clearly Madigin is not a crank, > > but there are many others who are also not cranks. Anybody who > > claims that Cantor's proof is false without identifying an error in > > the proof is a crank. > > In fact, your denial is integral to your dogma.
In fact, you really need to find something I have said which you consider false. Only then can I explain it to you.
> > LV

