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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: 5,426
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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.





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