EDB β€” 0F2

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Exercises

  1. [0F2](Proposed on 2022-12) Find two examples of \(a_{i,j}:{\mathbb {N}}Γ— {\mathbb {N}}β†’ {\mathbb {R}}\)

    • such that, for each \(i\), \(βˆ‘_ j a_{i,j} =0\), while for each \(j\), \(βˆ‘_ i a_{i,j} =∞\);

    • such that, for each \(i\), \(βˆ‘_ j a_{i,j} =0\), while for each \(j\), \(βˆ‘_ i a_{i,j} =1\).

    Can you find examples where moreover we have that \(|a_{i,j}|≀ 1\) for every \(i,j\)? [ [0F3]]

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  • convergence, of a series
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