On 25 Jan., 14:24, William Hughes <wpihug...@gmail.com> wrote: > On Jan 25, 10:01 am, WM <mueck...@rz.fh-augsburg.de> 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,
(Note this phrase: "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, ...
(Note that 1/9 is not actually existing as a decimal fraction.) > > > 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. > > January 25, 2013,
(One month after first Christmas after end of the world!)