Re: abundance of irrationals!)

Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx> wrote in message news:<ITSnetNOTcom#virgil-F94ABF.17110207042005@xxxxxxxxxxxxxxxxxxxxxxxx>...


> > > Cantor did not bother to define anything like that at all. He
> > > emphasized that for every positive whole number a_nn =/= b_n. That's
> > > all.
>
> I did not imply that CAntor invented that definition, only that he used
> it, as any mathematician of the time would have done.

Wrong. He did not.
> > >
>
> > > Your definition destroys Cantor's case. For a line number n = oo he
> > > would fail to identify a_nn.
>
> Where does Cantor ever mention a "line number n = oo"?

Cantor mentions it frequently. First it was called omega, later he
distinguished omega and aleph_0. But he definitely had no use for it
in his diagonal argument. Only you did introduce it here.

> > A line number n = oo? Where in the list would Cantor find a line with
> > such a "number"?

Nowhere!

Regards, WM
.

Quantcast