Unknown syntax with multiplication?

Question

So I have an assignment and this formula showed up:

$$\prod_{i<j} \;[\,p(j) - p(i)\,]$$

I have seen the multiplication sign before, I know what it is, but I don't know what '$i<j$' means in this context.

EDIT: I've looked all around the web for it, and I haven't found anything.

Answer 1

It means "the product over all pairs $i, j$ where $i < j$." For example, if $p(i)$ is defined for $i = 1, 2, 3$, then $$ \prod_{i<j} \;[\,p(j) - p(i)\;] = [ p(2) - p(1) ] [p(3) - p(1)] [p(3) - p(2)]. $$

Answer 2

It means the product of every version of the expression in which $i <j $ and $i $ and $j $ are in some set implied from context.

Answer 3

The notation indicates that you just should take the product for indices $i$ strictly less than some other index $j$. Surrounding context should indicate what $j$ is.

For example:

$j=4$

$$\prod_{i<j} p(i) = p(1) \times p(2) \times p(3)$$

Assuming your indexing starts from $i=1$. Hard to say more without context where the formula appears.