It does make sense in a mathematical context though. You might write something like p_S = \prod_{x \in S} x And then later find out that the set S contains on

It does make sense in a mathematical context though. You might write something like p_S = \prod_{x \in S} x And then later find out that the set S contains one element. Or it might even be the empty set in which case you'd interpret the above as equal to 1. This makes it work that p_{S union S'} = p_S p_S' in all cases.