```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 Gabrielused. 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.pdfOption 2: Cauchy Product          https://en.wikipedia.org/wiki/Cauchy_product#Cauchy_product_of_two_infinite_seriesThey give different partial sums. Option 1and 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 sumsare 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
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