In article <cf3382c6-62cf-4d77-905e-e11365075159@p16g2000yqd.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 30 Okt., 16:39, William Hughes <wpihug...@gmail.com> wrote: > > > > > Yes, if you assume that only finite sequences exist, then the list > > of all finite sequences contains all sequences. I am underwhelmed.- > > I do not assume that only finite sequences exist. But I do not see how > an infinite sequence d_oo can be reached by the sequences of diagonals > d_1, d_2, d_3, ... whereas b_oo cannot be reached by the sequence of > bottom lines.
That WM does not see something does not mean that it is not there to be seen, only that WM's vision is considerably less than perfect.
The diagonal sequence d_1, d_2, d_3, ..., is nested with d_n always a subset of d_(n+1), so the natural limit is the same as the union.
The sequence of bottom lines b_1, b_2, b_3, ..., are pairwise disjoint sets so its union is not like another line but a concatenation of disjoint lines, and has no equally natural limit..
