Date: Oct 6, 2017 12:51 PM
Author: bursejan@gmail.com
Subject: Re: Can two series, both diverges, multiplied give a series that converges?
I don't know what formal multiplication John Gabriel

used. You have different options:

Option 1: Algebra Product

MATH 304: CONSTRUCTING THE REAL NUMBERS,

Peter Kahn Spring 2007

http://www.math.cornell.edu/~kahn/reals07.pdf

Option 2: Cauchy Product

https://en.wikipedia.org/wiki/Cauchy_product#Cauchy_product_of_two_infinite_series

They give different partial sums. Option 1

and Option 2 have different sweep patterns:

Option 1:

A A B _

A A B _

B B B _

_ _ _ _

Option 2:

A A B _

A B _ _

B _ _ _

_ _ _ _

Exercise: Show that although the partial sums

are differently built (different sweep pattern),

the limit is the same, if it exists.

Am Freitag, 6. Oktober 2017 18:48:08 UTC+2 schrieb burs...@gmail.com:

> Depends, try it with the definition here:

>

> MATH 304: CONSTRUCTING THE REAL NUMBERS,

> Peter Kahn Spring 2007

> http://www.math.cornell.edu/~kahn/reals07.pdf

>

> See page 12, 4.2 Algebraic operations on sequences

>

> The lecture above expounds that when the first series

> {sn} converges (by Cauchy criteria) and the second

> series {tn} converges (by Cauchy criteria) , then the

>

> result {sn}*{tn} will also converge (by Cauchy criteria).

> If one of the series diverges then this theorem of

> the lecture above is no use for you.

>

> I would say everything is possible, like:

>

> oo * 0 = 0

>

> oo * 0 = oo

>

> oo * 0 = c

>

> oo * 0 = undefined

>

> Am Freitag, 6. Oktober 2017 18:24:33 UTC+2 schrieb konyberg:

> > One a goes to inf, the other goes to 0. What is now the product?

> > You can not tell if you do not know the functions defining the entities.

> > KON