In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 26 Nov., 00:56, Virgil <vir...@ligriv.com> wrote: > > In article > > <f6cde06f-8269-4768-a73e-9219bd020...@k6g2000vbr.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > Matheology 162 > > > > > About limits of real sequences. > > > > > The limit of an infinite sequence (a_k) of real numbers a_k is > > > determined solely by the finite terms of the sequence. Otherwise, the > > > limit would not have to be *computed* but would have to be *created*. > > > Analysis is concerned with analyzing, i.e., with finding. > > > > > To give an example, we can state with absolute certainty that in the > > > real numbers the sequence > > > 0.1, 0.11, 0.111, ... > > > has the limit 0.111... = 1/9. > > > > Unless we are give some assurance that the pattern that most of us see > > is the intended one, such as by formula, no one can state "THE" limit, > > as no such limit exists. > > Study real analysis. There are plenty of sequences which have one and > only one accumulation point. That is called *the* limit.
There are at least as many sequences which do not have any limit values of any sort, but even WM in his Wolkenmuekenheim cannot make them have limits that they do not have. > > > > > That is independent of the method which is used to analyze the > > > sequence. > > > > WRONG AGAIN! > > > > WM claims to be able to analyze a single sequence and, depending on > > which of two methods he uses, derive two quite different limits. > > No, I use the analytical method and accept the analytical result. I do > not accept deviating results. And mathematicians are invited to join > me.
But the non-analytical limit that exists for the sequence of sets of digit positions also exists and is quite different from what WM's delusions claim. --