On 4 Apr., 20:57, William Hughes <wpihug...@gmail.com> wrote: > On Apr 4, 8:30 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 4 Apr., 19:45, William Hughes <wpihug...@gmail.com> wrote: > > > > 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 exists which in > > > > principle are subject to induction but in fact 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. > > > If the collection is something else than all its elements, then you > > may be right. > > No, a collection is no more and no less than "all its elements".
But an inductive set contains elements that are not subject to induction?
> Note the "no less". A collection need not share a property > that every one of its elements has. In this case > every one of the elements of the collection has the property > that it can be removed without changing the union. > The collection does not have this property.
That is impossible if all elements can be removed. Compare the collection of three elements. If they are gone, the collection is empty - you may claim that then there is something remaining. > > [This holds for the "collection of all finite lines" > other collections, e.g. a "collection of three lines" > do have the property that they can be removed without > changing the union]-
Why do you think that there is a difference? Why do you not think (at least you have not yet mentioned it) that Cantor's argument also cannot exhaust the complete set?