When we introduce order in a set, we certainly are adding information to it: I have formed a set of three individuals I1, I2 and I3. As you suggest, order plays no role in it. Now I add order to it, forming them by size, from the smaller (let’s say I2), to the taller (let’s say I1). The resulting ordered set, or sequence, is E = [I2, I3, I1]. Do you think that the difference between the simple set and the ordered set, whatever it is, is a thing?