In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 5 Apr., 22:06, fom <fomJ...@nyms.net> wrote: > > On 4/5/2013 11:22 AM, WM wrote: > > > > > On 5 Apr., 12:08, William Hughes <wpihug...@gmail.com> wrote: > > > > >> More precisely. There is an infinite set of lines D > > >> such that any finite subset of D can be removed. > > > > > How do you call a subset of D that has no fixed last element? > > > > In set theory it is neither a set or a subset > > because the question does not make sense. > > In set theory a set can either be bijected with a FISON or not. > But what does it mean for a set to have not "fixed" last element? Does it men that that set has a non-fixed last element? While that would be nonsense outside of Wolkenmuekenheim, only WM can say what is allowed to go on inside Wolkenmuekenheim. > > A subset of D that can be removed without changing the union of the > remaining elements of D can be defined and makes sense. > Examples are the list D > 1 > 1,2 > 1,2,3 > ... > and the subset of the first n lines for every n in |N. > > So the question makes sense.
And the answer is that any subset of the set of FISONS of |N that is NOT co-finite in the set of FISONs of |n can be removed without diminishing the union of the set of remaining FISONs to less than |N. > > > One might compare the remark to a generic set > > of forcing conditions described by the > > information content of their initial sequences. > > No claptrap, please.
Why not from others when you are so free with your claptrap?
> Do you reject the theorem that every non-empty set of natural numbers > has a first element? Do you reject proofs by infinite descente? Do you > reject mathematics in favour of matheology?