On Apr 4, 6:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 4 Apr., 18:13, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Apr 4, 5:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 4 Apr., 16:01, William Hughes <wpihug...@gmail.com> wrote: > > > <snip> > > > > > If you remove "every finite line" > > > > your are removing an infinite thing > > > > "an infinite collection of finite things" > > > > If an infinite collection of infinite things exists actually, i.e., IF > > > it is not only simple nonsense, to talk about an actually infinite set > > > of finite numbers, then I can remove this infinite thing because it > > > consists of only all finite things for which induction is valid. > > > Nope. The fact that the collection contains only things for which > > induction is valid, does not mean induction is valid for the > > collection. > > And you believe that, therefore, always elements must which in > principle are subject to induction but in gact are not subjected to > induction?
Nope, just that you can have a collection where everything in the collection is subject to induction, but where the collection itself is not subject to induction.
You can remove any one thing that is in the collection. You cannot remove the collection.