In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 25 Jan., 09:24, William Hughes <wpihug...@gmail.com> wrote: > > On Jan 25, 9:02 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 25 Jan., 01:27, William Hughes <wpihug...@gmail.com> wrote: > > > > > > Outside of Wolkenmukenheim it is clear that an infinite set can be the > > > > union > > > > of finite sets.- > > > > > But in mathematics it is clear that a strictly increasing sequence > > > does not contain its limit. Each one of infinitely many terms fails to > > > reach the limit. And this case is given by the sequence of finite > > > initial segments of natural numbers. > > > > From which it follows that the collection of all natural numbers > > (which contains only finite natural numbers) > > is not a finite initial segment of natural numbers. > > > > So N is not a FISON. > > N, if actually existing, is the limit, the set of all natural numbers. > Similarly, 1/9 is not an element of the sequence 0.1, 0.11, 0.111, ... > > The limit 1/9 differs from all terms of the sequence, not only from > every term. > The limit N differs from all FISONs, not only from every FISON.
Can WM give an example of why he thinks that "from all x's" and "from every x" do not mean the same thing? --