EDB — 0F2

Exercises

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

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

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

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