On 7 Mai, 22:45, Virgil <vir...@ligriv.com> wrote: > In article > <656e14c3-aca7-4907-9487-89e9700ae...@m7g2000vbf.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 7 Mai, 21:47, Virgil <vir...@ligriv.com> wrote: > > > > > The union of lines > > > > cannot contain more elements than one line contains. > > > > Why not? > > > Because by construction all elements are in the last line already. > > What last line?
The last line would be that line that contains all natural numbers. If there is no last line, as it appears to be the case, then there are never all natural numbers. And never means never - not "in the infinite". > > The whole point of your partial diagram is that there is no last line,
> > > Unless there is some line that contains all other lines as subsets, > > > it is inevitable that the union contain more than any one line. > > > Obviously impossible in the list that I constructed. > > That is only because you did not finish your construction.