I completely understand the definition for the intersection between two or more sets, but this definition just does not make sense.
If M is a set of sets. For all A which are an element of M, x is an element of A. Isn't that the exact same thing as the union? Am I reading this wrong? I don't see how this definition covers the fact that x HAS to appear in EVERY A. It just states that x is an element of A, not every A.