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?
Piffle. Induction is valid for all elements of the inductive set. So the only thing that remains after elements are removed by applying induction is the set without any element.
> Induction is not valid for the collection, and you cannot > remove it without changing the union.
I do not remove "the collection" but I collect only all elements, namely every element which is subject to induction.
If you disagree, then name the first element of the finite lines that is not removed. Remember, the finite lines are enumerated by the natural numbers. And every non-empty subset of natural numbers has a first element.