On 12 Okt., 23:05, William Hughes <wpihug...@gmail.com> wrote: > On Oct 12, 5:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 12 Okt., 22:09, William Hughes <wpihug...@gmail.com> wrote: > > > > On Oct 12, 2:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > <snip> > > > > > If there R(oo) = aleph_0, a fixed number of > > > > circles, then mathematics requires the existence of a last line B(oo) > > > > with aleph_0 circles too. > > > > Absolute piffle. There is no such requirement. > > > You don't believe in the capacity of mathematics to calculate existing > > limits? > > No, I know that it is piffle to say that because a limit > exists you are required to add a line. >
You are not required to add a line. Only if you require that R(oo) contains a finished infinity of symbols, then you need a B(oo) with a finished infinite symbols.
If you do not require that nonsense, then you simply have potential infinity.
But you would like to have nonsense? For that sake you sacrifice logic?