On 23 Mrz., 01:08, Virgil <vir...@ligriv.com> wrote: > In article > <cab606ea-29e6-48ae-97c1-56cd1fd39...@f5g2000yqp.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 22 Mrz., 16:24, William Hughes <wpihug...@gmail.com> wrote: > > > > > And what is in your opinion beyond any finite set of lines? > > > > There is no such thing > > > as "beyond every finite set of lines". > > > Infinite sets are different from finite sets > > > but they do not contain anything > > > "beyond any finite set". > > > The decimal expansion of pi is not beyond any finite (i.e. rational) > > approximation? > > Since the decimal expansion of p is made up of digits in sequence, WM > needs to tell us which is the first of its digits tot exceeds finite > approximation? > --
If there is not more then all finite approximations, then there is no uncountability, because all rational approximations belong to a countable set.
Same holds for the FISONs of |N. Without a set that has more than every finite number of naturals, there is no uncountable power set of naturals.