In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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.
In your diagrams there were never any last lines.
And in the pattern you claimed to be following there could never be any last line until one could produce a natural that had no successor, which WMytheology, might allow but mathematics does not.
> If there is no last line, as it appears to be the case, then there are > never all natural numbers.
If there are all lines then there are all naturals, but neithe the sequence of naturals not the sequence of lines either requires or allows there to be a last one. > > > > The whole point of your partial diagram is that there is no last line, > > Of course.
Then the number of lines cannot be finite as any finite list of lines necessarily has a last line.
And equally the number of members of those lines cannot be finite as there is one new member for each new line and 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. > > I did all that can be done in mathematics.
What WM has done here is no part of mathematics, but is only part of his WMytheology.
In proper mathematics, a failure to define one's terms adequately, particularly when requested to do so, is regarded as a deadly sin which invalidates those claims, at least until those definitions are clarified and rid of their ambiguity.
WM deliberately commits that sin in virtually every post, because his WMytheological arguments, and he rarely makes any other kind, all require the deliberate ambiguity that his careful avoidance of clear definitions provides. --