In article <e2dbe64d-71da-44f6-8b54-99032ad9558c@b10g2000vbc.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 12 Okt., 23:28, Virgil <vir...@ligriv.com> wrote: > > In article > > <b48b1b4d-0b1d-4b84-beb7-334d50516...@z19g2000vby.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 12 Okt., 21:27, 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. > > > > > So you reject the theorem: > > > > > Forall n in |N: H(n) = B(n) = R(n) > > > and the limit exists (you say so) > > > then H(oo) = R(oo) = B(oo) > > > > While that may be true in WM's mythematics, it need not be true in > > mathematics. > > > > WM has provided the counterexamples himself: > > > > At t = -1/2^n, balls numbered 10*n -9 to 10*n are put into an initially > > empty vase and a ball is then removed. > > > > Depending on the rule by which that ball is removed, A(remove the lowest > > numbered ball), or B(remove the highest numbered ball),, at t = 0, n = > > oo, the vase can be either empty, A(oo) or contain infinitely many > > balls, B(oo). > > > > But card(A(n)) = card(B(n)) for every finite n. > > And that example serves as an "explanation" or even a "justification" > in your opinion?
It certainly justifies card(A(n)) = card(B(n)) for every finite n and also card(A(oo)) =/= card(B(oo)) --
