Inspired by Raghav Vaidyanathan

For $i, j \in \mathbb{N}^+$ , let $a_{i,j} = \begin{cases} \frac{ 1}{i \times j } & i < j \\ 0 & i \geq j \\ \end{cases}$ .

What is the value of

$\sum_i \sum_j a_{i,j} - \sum_j \sum_i a_{i,j} ?$

Inspiration