To continue with your example, take cases where a (finite) collection of discrete objects is summed over (unioned over, whatever). You'd let N be the number of

To continue with your example, take cases where a (finite) collection of discrete objects is summed over (unioned over, whatever). You'd let N be the number of such objects, and then twenty following pages of text would contain summations from 1 to N. This is more compact than summations from 0 to N-1. And in a certain sense, there's one less "token" to remember (i.e., if you start at 1, you have 1 and N to remember, but when you start at 0, you have N, 0, and N-1 to remember). The one that's more compact tends to be discipline-specific.