In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 12 Apr., 01:14, Virgil <vir...@ligriv.com> wrote: > > > > Let the list contain all binary sequences q_k. > > > > That is assuming something that is false, > > No, it would be false only if Cantor was right. But he fails. > Nevertheless, since there is no binary sequence defining any > irrational number: Let L be the list of all binary sequences that can > be interpreted to define rational numbers of the unit interval.
Every irrational of form 1/sqrt(prime) defines one of the binary sequences that WM claims do not exist, as do lots of other well-defined irrationals.
But nowhere outside of Wolkenmuekenheim is being defineable a necessary requirement for existing. > > > > > > The counter-argument can be written: > > > For every n: (d_1, ..., d_n) does not differ from infinitely many > > > entries (qk1, ..., qkn) with k > n.
But it does not counter anything having to do with infinite sequences because it does not say anything about any infinite sequences. > > > > Does "(qk1, ..., qkn)" mean > > "(q_k1, ..., q_kn)" > > or "(qk_1, ..., qk_n)" > > or something else entirely? > > All these notations can be used.
Then why use one that is inconsistent with your immediately prior "(d_1, ..., d_n)"?
The use of such a differing notation certainly suggests a differing meaning.
> Meant is: the first n bits of the k-th sequence.