Re: Set Products Question

Hey Aryth.

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).

Re: Set Products Question

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 ).

Re: Set Products Question

Quote:

Originally Posted by

**Aryth** 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??

No, they are not. The second assumes a finite number of sets (n) while the first does not.