|
|
On Sat, 30 Jul 2005 08:18:45 -0400, A N Niel
<anniel@xxxxxxxxxxxxxxxxxxxxx> wrote:
>In article
><12708828.1122723804279.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
>Xantos <xantos_2005@xxxxxxxxx> wrote:
>
>> Hello,
>>
>>
>> Nets are generalized sequences. In the same manner
>> series can be generalized. I don't know it they also
>> have some fancy name.
>>
>> If the generalized series Sum_i(x_i) converges,
>> then it is easy to show that the net
>> (x_i) is a zero-net.
>>
>> But what I really would like to know is whether
>> in that case at most countably many x_i's are different from zero. That is to
>> say, the summation can be
>> done only on countable subset of I.
>> Thank you for your comments.
>>
>> Xantos
>
>If a series of reals converges, then all but countably many are zero.
What's the _definition_ of Sum_i(x_i) that you're assuming he's
referring to here? My impression is that the x_i are indexed
by some directed set, and I can't figure out what that definition
should be.
(If we were talking about sums indexed by elements of _sets_ I
can imagine what the definition has to be.)
>Series with some other values (say a topological vector space) need not
>have this property.
************************
David C. Ullrich
|
|