On 28 Nov., 14:56, mstem...@walkabout.empros.com (Michael Stemper) wrote: > In article <f6cde06f-8269-4768-a73e-9219bd020...@k6g2000vbr.googlegroups.com>, WM <mueck...@rz.fh-augsburg.de> writes: > > >Matheology =A7 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. > > That is correct. Since the a_k are chosen from the real numbers, and since > all real numbers are finite, all of the a_k are finite, and the sequence > has no infinite terms. > > Now, depending upon the nature of the sequence, the terms may increase > without limit, which is one way of having a real sequence that has no > well-defined limit. That doesn't change the fact that each and every > term is still finite.
Anyhow: Analysis and set theory supply different limits, namely a limit larger than 1 and a limit less than 1. That's the point.