On 5 Mrz., 12:45, William Hughes <wpihug...@gmail.com> wrote: > On Mar 5, 10:57 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 4 Mrz., 23:56, William Hughes <wpihug...@gmail.com> wrote: > > > Let K be a (possibly potentially infinite) set of > > > lines of L. Then > > > > Every FISON of d is in a findable line of K > > > iff K does not have a findable last line > > > No, false quote. > > What do you think this was a quote of?
One of my statements.
> This is my claim, put into the language we > have now developed. > > >Every findable FIS of d is in a findable line of L > > Clearly,
Fine. Nevertheless I would like to emphysize the identity. Unfindable FIS of d do not correspond to findable lines. As well as unfindable lines do not correspond to findable FIS of d.
> The question is: "For what subsets of lines > of L is this still true?" Hence the condition > on K
The question is: How can anybody claim that, in actual infinity, an infinite set of lines is required to house all FIS of d???
It is obviously one of the simplest mathematical proofs to show by induction: If line n is not the last line, then line n is not required.
Therefore, if the set has no last line, then *no* line is required to house all FIS of d. A contradiction? Only if "all FIS of d" are claimed to exist.