Does your combination contain all permutations Ai X Bj for all possible i and j or is i = j? (The way you have written it is unclear).
I'm beginning a section on Product Topologies and I have to do a few problems, but I'm not seeing the difference between these two.
Let and be two nonempty families of sets. Prove that:
Suppose that and are sets. Prove that:
Aren't these asking for the same thing??
To be honest I can't answer that question. The problems are exactly as I have typed them. In the proofs... I imagine that the equations would hold either way (Sets under intersections commute, so I can order them however I like on the right hand side and arrive at any necessary permutation as long as it's ).