In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 17 Apr., 21:33, Virgil <vir...@ligriv.com> wrote: > > > > Is there any number of A that is not in at least one line? > > > > The set A in not "in" any one line so the set A is not in B. > > I did not ask about the set A, because it will turn out that there is > no such set, if one is willing to accept that nothing of the set > remains, after all its elements have been removed.
On that basis, no set can exist.
But as set theories do exist, perhaps removing all the elements from a set does not mean that the original set did not exist.
Nicht wahr? > > > > > So we have an identity. There is no actually infinite line in B, so > > > there is no actually infinite sequence A. > > > > At least not as a term of B. > > So it is. But it is trivially true that every element of A together > with all its predecessors is in a line.
True but irrelevant.
To say that some subsets of one set are subsets of another does not make all of them subsets of the other, and A is neither a subset nor a member of B. > > The argument is similar to: (A < B & B < C) ==> (A < C), well-known > and often applied in mathematics.
It is not similar enough > > > While WM claims that there is no set A, > > I don't claim it. I prove it.
WM has not proved it yet!
At least not with any arguemnt valid outside of his hideaway from logic, Wolkenmuekenheim. --