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
In set theory a set can either be bijected with a FISON or not.
> because the question does not make sense. >
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.
> One might compare the remark to a generic set > of forcing conditions described by the > information content of their initial sequences.
No claptrap, please. The definition is clear: We consider any subset of D that can be removed without changing the union of the remaining elements of D. Does the remaining set of lines have a first line- number? 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?