In article <firstname.lastname@example.org>, WM <email@example.com> 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.
-- Michael F. Stemper #include <Standard_Disclaimer> A bad day sailing is better than a good day at the office.