What does $\prod_{i<j} (j - i)$ mean where $i,j\in\{1,2,\ldots,8\}$?

Question

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.

Answer 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 $$\prod_{j=2}^8\prod_{i=1}^{j-1}(j-i).$$

Answer 2

It denotes the product of all factors $j-i$ where $(i,j)$ ranges over the set $$\{(i,j)\mid i,j\in\{1,2,3,4,5,6,7,8\}\wedge i<j\}$$

Observe that there are $\binom82=28$ factors.

Answer 3

It is more clearly denoted $$\prod_{\substack{1\le i,j\le 8\\i<j}}(j-i).$$