On 23 Nov., 23:32, Virgil <vir...@ligriv.com> wrote: > In article > <196a9e2e-96c9-4814-a3e6-4c2fd795c...@m13g2000vbd.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > Clear mathematical formulas are not handwaving. > > I have yet to see any "clear mathematical formulas" which can explicitly > display a sequence that has no beginning.
The sequence has no ending. In decimal represenation, i.e., representing only the coefficients, we write from right to left. > > > > An analytical expression of infinity is this > > Limit[n-->oo] SUM[k=0 to n] a_k*10^k = oo > > Not as it stands! You would have to first establish that at least > infinitely many of those a_k's are to be strictly positive.
I did that. I wrote: ..., a_k, ..., a_3, a_2, a_1, a_0 where for every k there exists a digit a_(k+m) =/= 0, with m in |N.
> > > > > 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. Obviously then also the representation has to be extended from a finite number of digits to an infinite number.