In article <email@example.com>, WM <firstname.lastname@example.org> 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.
> That is independent of the method which is used to analyze the > sequence.
WM claims to be able to analyze a single sequence and, depending on which of two methods he uses, derive two quite different limits.
But of course, he is, as usual, working exclusively in Wolkenmuekenheim, to which no one sane has access. --