Re: * says: Definition: sum{i in N} i = 0

WM wrote:

On 8 Jun., 10:34, Franziska Neugebauer <Franziska-
Neugeba...@xxxxxxxxxxxxxxxxxxx> wrote:

I think you should know that a divergent positive series cannot
have the sum 0.

A divergent series does not possess a defined value within the
framework used to determine its divergency at all.

A divergent series has the property of being divergent, which is but
another way of saying that it has no finite value

This is not correct. If have learned something like that:

http://en.wikipedia.org/wiki/Divergent_sequence

Therefor "divergent" simply means there is no L e M which is _limit_
according to the usual rules of limits.

You or *** may (for whatever purpose) hence define ad lib which is
perfectly legal. Whether it is useful is a another issue.

which in turn implies that is has not the value 0

non sequitur.

which implies that ***'s definition is wrong

non sequitur. (Euler/Ramanujan et al. would be "wrong" either).

after the divergence has been shown. One way to do
this is to start with Niole d'Oresme.

Another is to stop with him right now.

Because: If it could, then also Cantor's diagonal number
could have the same value as thirteen different entries of his
list, or, to put it in other words, then the concept of infinity is
as mad as the madmathics of its adherents.

The diagonal number possesses a defined value since it _is_
convergent.

Yes, and it converges to a real number which is an entry of the
infinite list, because (a_i - b_i)*10^-i = 0.

It has already been in depth explained to and ignored by you that
the diagonal number has a convergent series, i.e. that its limit exists
and that the limit is not in the list.

Here is an example which might enlighten you: Consider the list of
decimal approximations of pi:

Of what?

F. N.
--
xyz
.

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