In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 6 Apr., 23:17, William Hughes <wpihug...@gmail.com> wrote: > > On Apr 6, 11:04 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 6 Apr., 22:30, William Hughes <wpihug...@gmail.com> wrote: > > > > > > My claim is: > > > > > > Let D be the set of all lines, and let > > > > E be any one finite subset of D. > > > > Then D\E is not empty. > > > > > Your claim is true. > > > > I also claim: Let D be the set of all > > lines, then if you remove any one finite > > subset of D there is something left. > > I remove the union of all finite subsets because for all n there is an > n+1. (The union of finite subsets can never be actually infinite, > because for every n, the number of FIS is finite.)
The union of the set of all finite subsets of any set, S, is the set S itself.
So if S is actually infinite, so is the union of the set of all S's subsets. --