Q: Convergence of double sum and its rearrangement Let $A=\sum_{i=1}^{\infty}\sum_{j=1}^{\infty}a_{ij},a_{ij}\geq 0$ and $$\phi:\mathbb N \to\mathbb N\times\mathbb N$$ be any bijection. Now $B=\sum_{k=1}^{\infty}a_{\phi(k)}$.
How $A$ and $B$ are related.  My intuition tells both series converges are diverges together and if converges, they converges to same value. But I didn't able to prove this. Please give sketch o the proof.
Also, how the converges of both series related if $a_{ij}$ are not necessarily non negative. 
