I'm just don't get this question.(adsbygoogle = window.adsbygoogle || []).push({});

from my text:

[tex]define\ t_{mn}\ =\ \sum^{m}_{i=1}\sum^{n}_{j=1}|a_{ij}|,[/tex]

[tex][a_{ij}\ is\ a\ doubly\ indexed\ array\ of\ real\ numbers.][/tex]

[tex](a)\ prove\ that\ the\ set\ \{t_{mn}\ :\ m,n\ \in\ N\}\ is\ bounded\ above.[/tex]

[tex](b)\ use\ (a)\ to\ conclude\ that\ (t_{nn})\ converges.[/tex]

This has been confusing me for a couple of days, i've got the rest of the proof, but this part doesn't make any sense. The theorem i'm trying to prove states "IF the doubly indexed array converges absolutely," but if I "prove" {t_mn} is bounded, it suggest then that every doubly indexed array would converge absolutely, so i'm not sure how i can possibly answer (a).

From what i understand, the set {t_mn} is all the possible outcomes of the double summation, for instance, the first member would be a_11, the second might be a_11 + a_12 or a_11 + a_21, etc. But that set has no bound. It can grow as much as it wants, i think.

i'm not sure where i'm going wrong here. please help, thanks.

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# Double Index Array

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