On Oct 14, 3:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 14 Okt., 18:56, William Hughes <wpihug...@gmail.com> wrote:
> > Piffle. L does not change depending on whether it is a > > maximum or a st upremum. > > No, L does not change. But there is a difference between maximum and > only csupremum.
Indeed, the way you are using the words, L is a maximum if it is in the "infinite triangle" and a supremum if it is not in the "infinite triangle". Whether L is a maximum or supremum has nothing to do with the sequences (which are defined by the finite triangles). Since a limit may or may no preserve symmetry, you cannot use symmetry to argue that the same thing must happen in all three cases.