On Oct 23, 5:27 am, WM <mueck...@rz.fh-augsburg.de> wrote: > On 23 Okt., 02:49, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Oct 22, 5:55 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > <snip> > > > > > > Is it a maximum or only supremum? > > > > > To determine this you have to determine if the limit > > > > is in the infinite "triangle". There is no reason > > > > to expect the answer to be the same in both cases. > > > > There is no reason to expect the limit of > > > 1, 2, 3, ... > > > and of > > > 1, 2, 3, ... > > > to be the same in both cases. I understand. > > > The limit is the same in both cases. However, you asked if the > > limit is a maximum or a supremum. In the way you are using the > > terms, the limit of the diagonals of the finite triangles is a > > maximum, if and only if, the infinite "triangle" has a diagonal, > > while the limit of the last lines of the finite triangles is a maximum > > if and only if the infinite "triangle" has a last line. > > By identity of all finite terms of the sequence we see that both cases > are identical. It is impossible to judge about the limit by looking at > the limit because we cannot oversee it. > > > There is no reason to assume that the questions "Does the infinite > > "triangle" have a diagonal?" and "Does the infinite "triangle" have > > a last line" have the same answer. > > There is no reason that these limits exist. > But if they exist, then there is no chance to give differing answers.
Nope. The infinite "triangle" has a diagonal but does not have a last line.
> At least, there is no reason with foundation in mathematics. In > mathemtics limits are completely defined by the finite terms. >
Nope, the question of whether a limit is a maximum or a supremum is not determined by the finite terms of the sequences involved, the sequence of the diagonals of all finite triangles plus the diagonal (if it exists) of the infinite "triangle" and the sequence of the last line of all finite triangles plus the last line (if it exists) of the infinite "triangle".
