On 20 Feb., 13:31, William Hughes <wpihug...@gmail.com> wrote: > On Feb 20, 12:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 20 Feb., 11:30, William Hughes <wpihug...@gmail.com> wrote: > <snip> > > > A statement you can make is that there > > > is no line of the list with the property > > > that it is coFIS to d. > > > (you do not need every line or every FIS to "actually > > > exist" to make this statement) > > > You need all FISs of d to make this statement. > > No, for each line of L you only need some > of the FISs. For every line you need every > not all.
Then you have a statement for finitely many lines and none for infinitely many lines. > > <snip> > > > > Let z be a potentially infinite sequence such that > > > for some natural number m, the mth FIS of > > > z contains a zero. > > > > Are z and x coFIS? > > > No. > > Is the following statement true > > For every natural number n we have > > the (n+1)st FIS of the nth line > of L contains a 0.
Of course. Similarly we have "for every natural number there are infinitely many FIS of infinitely many lines that do not contain a 0".
Again: Do not confuse every and all. After "all natural numbers" no natural number is following. After every natural number, there are infinitely many natural numbers following.