In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 12 Okt., 22:09, William Hughes <wpihug...@gmail.com> wrote: > > On Oct 12, 2:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > <snip> > > > > > If there R(oo) = aleph_0, a fixed number of > > > circles, then mathematics requires the existence of a last line B(oo) > > > with aleph_0 circles too. > > > > Absolute piffle. There is no such requirement. > > You don't believe in the capacity of mathematics to calculate existing > limits? > > If three sequences are identical for every n, then the limits are > identical (in mathematics). > > Forall n in |N: H(n) = B(n) = R(n) > and the limit exists (you say so) > then H(oo) = R(oo) = B(oo) > > Didn't you learn that during your education?
Since it is false, I am glad not to have done so.
The rile by which the numbers H(n), B(n), and R(n) are calculated can be the same for every finite n and different for aleph_0.
WM himself provided the example proving him wrong :
At time -1/2^n insert balls 2*n-1 and 2*n unto the initially empty vase and take one out. The number of balls left in the urn at t = 0 will depend on the rule determining WHICH ONE is to be taken out, and can produce any value from zero up to and including aleph_0. --