Le 26.11.2012 07:38, WM a écrit : > 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.
What is properly amazing, and shamefull, is that WM is actually teaching math in an academic german institution while confusing having several accumulation points for a sequence (for a given topology) and having different limits for different topologies.