In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> > > in any case the limit of my sequence > > > > > 01. > > > > > 0.1 > > > > > 010.1 > > > > > 01.01 > > > > > 0101.01 > > > > > 010.101 > > > > > 01010.101 > > > > > 0101.0101 > > > > > ... > > > has infinitely many digits right to the point as well as left to the > > > point. > > > > If the limit of your sequence were a real number then it would NOT have > > any such representation, and only real numbers do have such any basal > > representations > > The limit is not a real number, but an element of the extended reals.
The only standard representations of any additional members of the extended reals, over and above the members of the standard reals, at least outside of Wolkenmuekenheim, are oo, +oo and -oo.
> Obviously then also the representation has to be extended from a > finite number of digits to an infinite number.
What is "obvious" in Wolkenmuekenheim is often not even true elsewhere. --