"G.E. Ivey" <george.ivey@gallaudet.edu> wrote in message news:19682293.1167501710592.JavaMail.jakarta@nitrogen.mathforum.org... > > > > In this case also ,the process doesn't end.I > > understand your argument,and > > understand Cantor's argumment,but still now I wonder > > that all reals are > > listed? > Perhaps I am misunderstanding but the whole point of Cantor's argument is that the set of all reals CAN'T be "listed": that is cannot be put in a list so that we could label the numbers 1, 2, 3, ... > Yes, that the set of all reals can't be listed, is what Cantor intended.That I mentioned to Cantor was inapropriate. And about my statement above that all reals are listed ,I admit my argument was mistaken. My question is wheathr what cannot be numbered really exist or not.
> >We cannot take up all reals arbitralily for > > the reason that even if > > we take up any real number ,there is larger real > > number. > Which just says that the set of all real numbers is unbounded. That happens to also be true for the set on integers and doesn't have anything to do with your argument up to this point. > Sorry, my explanation was not good. And though it stands for in the meaning you said above, what I wanted to say ,is that we can only take up countable reals from among all reals. And we can only say about the rest of reals,that they exist,but cannot discribe them in any way.
> > And yet the amount of members of set (?) are > > compared. > What do you mean by "compared"? Compared to what? > > > > You believe there is, but it does not follow from > > the > > > mathematics. It follows from something else. > > > > > > - Randy > > > > > Regards > >
