Re: *1* says: Definition: sum{i in N} i = 0

In article <1182325047.007090.132530@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 20 Jun., 00:09, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1182257430.850848.213...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 17 Jun., 16:06, Franziska Neugebauer <Franziska-
Neugeba...@xxxxxxxxxxxxxxxxxxx> wrote:
WM wrote:
On 16 Jun., 00:45, Franziska Neugebauer <Franziska-
Neugeba...@xxxxxxxxxxxxxxxxxxx> wrote:

The "reciprocal method" does not attach a defined value to the
undefined symbol sum_{i e N} a_i: The reciprocals' limit is 0 hence
the limit has form "1/0" meaning "undefined" to anybody.

I am sorry

The sorriest!



Even if this rule were correct "1/0" is still undefined according to the
orthodox mathematics in the absense of more advanced definitions.

Therefore we do not say the limit is 1/0 but we state: If the sequence
of reciprocals has limit 0, then the improper limit of the sequence is
oo or oo or it is alternating.

Since the point is not limits of sequences but of series, WM is sorry
again.

Series can be treated (and, in mathematics, are treated) as sequences
of their partial sums.

The definition of the limits of series is defined in terms of the limit
of its sequence of partial sums, but beyond that, they are quite
distinct.
.

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