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. > > > 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.