In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 23 Nov., 20:54, William Hughes <wpihug...@gmail.com> wrote: > > > Well, looks like communication > > has come to a halt. > > > > You are correct, if analysis requires > > that oo be described by digits > > then there is a contradiction in mathematics. > > I see no way of convincing you that oo > > cannot be expressed by digits, nor have > > you given any evidence other > > that vague handwaving that it can. > > 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. > > 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.
> > 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 > > So it is incorrect to say that communication has come to a halt but it > is correct to say that you have no further arguments to defend your > position but do not want to admit that for reasons that I don't know.
Those reasons have been quite clearly and repeatedly represented.
That WM remains ignorant of them, or at least clams to, is only by his own choice, rather than by any necessity. --