In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 8 Apr., 13:18, William Hughes <wpihug...@gmail.com> wrote: > > On Apr 8, 12:56 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > You can remove a finite set of lines without removing the > > > infinite set. That is obvious. But why should it not be possible > > > to remove all finite lines? > > > > I said the "collection of all lines" (this is the same as the > > "collection of all finite lines"). The collection of all finite > > lines is D and it is not possible to remove D without leaving the > > empty set. > > That is not in accordance with your statement: "Because the fact that > for every finite union P is true, says nothing about whether P is > true for an infinite union."
It is not in contradiction to it either, so do you have a point or ar you just being your usual obnoxious self?
> > Remember the definition of actually infinite for that case: The > number of indices in 0.111... is larger than every finite number of > indices and therefore cannot be reached by a sequence that contains > only finite numbers of indices. 0.1 0.11 0.111 ... Therefore it > cannot be removed by removing all finite lines.
The issue is whether there are anything other than finite lines in that set of lines. And the set being infinite does not require that any line be infinite.
Every line is finite, even when that set of lines is not finite, so removing every finite line removes every line. > > In order to proceed, you have to assume
WE do not have to assume anything more than what we actually have.
WM has to assume that one cannot have an infinite set without having an infinite member in it, which everyone else knows is contrary to fact, --