User blog:Mr. Junky/Question about BEAF

So I have had this question for a while.

I know that {a,b,c} is a(b \(\uparrow)s) to c

But when it does something like {a,b,c,d) I have no idea how d affects this number. How exactly does d change {a,b,c}?

Thus I have a question. In simple terms, how exactly do entries beyond the 3rd entry change the number being defined. We can do {a,b,c,d,e} but then how does e change {a,b,c,d) and we can do {a,b,c,d,e,f} but then how does f change {a,b,c,d,e} and so on? In arithmetic terms please.