The set A has elements a. For any given element a, there must be an equivalent element b in set B.
For any a and b pair, there must be a element c in C.
For each element in C, there must be an equivalent element in D and for each pair in C and D there must be a element in E. This keeps going, so for each pair there is a pair which needs a pair and so on.
My question is how I describe this mathematically, and how do I prove that the set of all such sets cannot be finite?