On Apr 5, 7:56 am, WM <mueck...@rz.fh-augsburg.de> wrote: > On 4 Apr., 23:08, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Apr 4, 10:45 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 4 Apr., 20:57, William Hughes <wpihug...@gmail.com> wrote: > > > <snip> > > > > > 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. > > > Nope. Any single element can be removed. This does not > > mean the collection of all elements can be removed. > > Does the axiom of infinity result in an infinite set?
It says that an infinite set exists.
Your problem is that you are using
If a collection of lines C cannot be removed then there is a line in C that cannot be removed.
However, this is only true for finite collections. For an infinite collection
There is an infinite collection of lines, D, that cannot be removed, however, any single line of D can be removed.
You do not like this property of infinite collections but it is not a contradiction.