Date: Nov 14, 2012 3:28 PM
Subject: Re: Cantor's first proof in DETAILS
Zuhair <firstname.lastname@example.org> wrote:
> On Nov 14, 10:18 am, Uirgil <uir...@uirgil.ur> wrote:
> > In article
> > <6a63fbfd-f7e7-458f-af65-fae2c805c...@d17g2000vbv.googlegroups.com>,
> > Zuhair <zaljo...@gmail.com> wrote:
> > > On Nov 14, 12:45 am, "LudovicoVan" <ju...@diegidio.name> wrote:
> > > > "Zuhair" <zaljo...@gmail.com> wrote in message
> > > >news:email@example.com...>
> > > > On Nov 13, 11:16 pm, Uirgil <uir...@uirgil.ur> wrote:
> > > > <snip>
> > > > >> Your alleged argument against the Cantor proof does not work against
> > > > >> either Cantor's proof, nor Zuhair's proof, nor my proof for that
> > > > >> matter,
> > > > >> since your N* is irrelevant for all of them.
> > > > > I showed in the Corollary that even if he use N* as the domain of
> > > > > (x_n), still we can prove there is a missing real from the range of
> > > > > (x_n). So Cantor's argument or my rephrasing of it both can easily be
> > > > > shown to be applicable to N* (any set having a bijection with N) as
> > > > > well as N.
> > > > You are simply missing the point there: we don't need N* to disprove
> > > > Cantor,
> > > > we need N* to go beyond it and the standard notion of countability. In
> > > > fact, that there is a bijection between N* and N is a bogus argument
> > > > too,
> > > > as
> > > > the matter is rather about different order types.
> > > > -LV
> > > Now I think I'm beginning to somewhat perhaps understand your
> > > argument. I think (I'm not sure though) that what you want to say is
> > > that when we are having arguments with "LIMITS" then we must design
> > > the whole argument such that the Limit comes from the sequence, and if
> > > this design was not made then the argument is inherently deficient as
> > > far as the truth of inferences derived from it is concerned. So what
> > > you are trying to say is that Cantor's argument began with incomplete
> > > arsenal so it ended up with misleading inferences. You are making an
> > > argument at TRUTH level of the matter, and yet it is concerned with
> > > formal technicality as well, which is an argument beyond the strict
> > > formal technicality.
> > > Anyhow if I'm correct, this form of reasoning for it to stand the
> > > quest, then there must be a clear line of justification for it. For
> > > instance the argument about whether the reals are countable actually
> > > means literally whether there is a bijection between the reals and N,
> > > so N is at the heart of the subject. Now to go and say that
> > > countability of the reals (which means bijectivity of reals to N) can
> > > only be reached about by circumventing N and using another countable
> > > infinite set N* as the domain for any sequence in an argument using
> > > limits is really strange somehow.
> > It is worse, mathematically speaking, than merely strange, it is
> > nonsense.
> > > What you are having is the following:
> > > When we use N as the domain of injections (x_n), (a_n) and (b_n),
> > > then Cantors argument PROVES and SHOWS that there is a real that is
> > > not in the range of those functions.
> > > When we use N* as the domain of injections (x_n), (a_n) and (b_n),
> > > then Cantor's argument will seize from working in the same way to show
> > > the missing real.
> > ?"Cease"?
> Yes, Cease, i.e. stop, of course I'm speaking about stopping in the
> sense of running the exact particulars of the argument per se, that's
> why I said "...in the same way" for example when you use some N* which
> has an omega_th position as the domain then for example Result 7
> cannot be proven in exactly the same straightforwards way as it is
> proved with N, to prove it you need to define it indirectly in terms
> of bijections from N* to N ...., which is a long way. But ultimately
> you will also succeed in finding a missing real as I pointed out. That
> is merely a temporary conundrum with the argument that has no
> significance to the reality of the matter, and has no philosophical
> value whatsoever.
You wrote "seize". I was merely asking if you meant "cease".