I like your exposition but also want to defend formal notation :) Formal notation is great because it lets you compare different constructions side-by-side, manipulate them (incl. building upon earlier constructions - "same as above except A_i = ..."), etc whereas prose is less suited for that. Once your eye gets used to it, it is much much more efficient at conveying various details. (Akin to (a + b)^2 = a^2 + b^2 + 2ab vs "If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the rectangle contained by the segments." (Euclid, Elements, II.4, 300 B.C.))