What does $\prod_{i<j} (j - i)$ mean where $i,j\in\{1,2,\ldots,8\}$?
What does $\prod_{i<j} (j - i)$ mean, where $i$ and $j$ are values from the set $\{1,2,3,4,5,6,7,8\}$ ?
I know how the capital pi product works, but I have never seen it with nothing on top and an inequality on the bottom.
Solution 1:
It means that we're multiplying factors $j-i$ where $i<j$ and $i,j\in\{1,2,3,4,5,6,7,8\}.$
Put another way, it is $$\prod_{j=2}^8\prod_{i=1}^{j-1}(j-i).$$