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Topic: The objects that Newton played with were called infinite series
but had ZERO to do with infinity. The name infinite series is a misnomer.

Replies: 2   Last Post: Oct 3, 2017 5:15 PM

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 bursejan@gmail.com Posts: 5,511 Registered: 9/25/16
Re: The objects that Newton played with were called infinite series
but had ZERO to do with infinity. The name infinite series is a misnomer.

Posted: Oct 3, 2017 5:15 PM

Can you make an example, where two series cannot
be multiplied formally, independent of their
convergence?

For the case of Cauchy product:

s_n = sum_i=1^n a_i
t_n = sum_i=1^n b_i
(s*t)_n = sum_i=1^n c_i
where c_i=sum_k=1^i a_k*b_(i+1-k)

For the case of algebra product:

s_n = sum_i=1^n a_i
t_n = sum_i=1^n b_i
(s*t)_n = s_n*t_n

Am Samstag, 30. September 2017 23:59:43 UTC+2 schrieb John Gabriel:
> On Saturday, 30 September 2017 13:42:44 UTC-5, burs...@gmail.com wrote:
> > Formally you can multiply two series, even if they
> > are not coverging.

>
> Tsk, tsk. No. You cannot do infino-sero arithmetic with series that do not converge. Period.

Date Subject Author
10/1/17 zelos.malum@gmail.com
10/3/17 bursejan@gmail.com