In article <email@example.com>, 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. > > Zuhair
You wrote "seize". I was merely asking if you meant "cease".