On 3/18/2013 6:59 AM, WM wrote: > On 18 Mrz., 00:59, Virgil <vir...@ligriv.com> wrote: > >> >> Why does WM claim that after what WM calls "Cantor's list" has been >> diagonalized, he can include all anti-diagonals, when it is always >> possible to find others that have been so far overlooked? > > This simply and exactly shows that it is inconsistent to assume one of > both powers to be stronger.
What it shows "simply and exactly" is that you do not understand the argument of Cantor diagonalization.
> > Every list yields another diagonal. > And every diagonal can be included in another list.
You are assuming the directed set structure of the natural numbers. That is well-established.
> > Both these facts are the two sides of infinity.
Notice the reference to infinity in the sense of a singular identifying term.
> Cantor did that false > step to choose one as more justified than the other.
To be precise, Cantor to the step (truth and falsity are irrelevant) to treat infinity with the same justification as one treats 0.
That is why the null class trivially satisfies the idea of a limit ordinal.