In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 19 Jul., 02:58, Virgil <vir...@ligriv.com> wrote: > > In article > > <ac5f46d7-5bb0-4166-8731-f3d224209...@q2g2000vbv.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 18 Jul., 21:53, Virgil <vir...@ligriv.com> wrote: > > > > In article > > > > > > The Lim-Sup and Lim-Inf definitions depend only on the existence of a > > > > sequence of sets, which is what the Vase problem provides. > > > > > Simultaneously, also the approximations of the continiued fraction > > > ((((((10^0)/10)+10^1)/10)+10^2)/10)+... > > > happen to provide the same sequence of sets. > > > > Nonsense! None of those approximations are sets at all, but merely > > rational numbers. > > You can read them as natural numbers. But if not?
They are not any notation for sets that is in common usage, so that they are not sets until your private usage is explicated. > > > > > > > > > Does set theory provide the value of the continued fraction? > > > > No more than continued fractions provide set limits. > > > > Only someone as ditzy as WM would conflate those two types of sequences. > > And what is this sequence? > > > 0 1 > 0 . 1 > 0 1 0 . 1 > 0 1 . 0 1 > 0 1 0 1 . 0 1 > 0 1 0 . 1 0 1 > a n d s o o o o o n > > Is it a sequence of sets or of real numbers?