Partially Ordered Set, example from Wiki.

Hi,

I was reading in the Naive Set Theory book by Halmos, and encountered partially ordered sets.

It seems like a lot of people understand these things immediately. I am not one of those :)

I did a bit of searching and read through the wiki on posets. Here's an example they give:

Set of natural numbers equipped with the relation of divisibility.

is the set of all positive divisors of 60.

Then this relation (divisibility) is reflexive, transitive and antisymmetric.

(1)Reflexive:

So,

As I understand it, the ordered pair is in a partially ordered subset of .

Now, I guess I can "create" these ordered pairs by taking the Cartesian Product, .

This gives me among other things the diagonal terms , all in all 11 diagonal terms.

I can then go ahead and create a subset of A that is reflexive:

perhaps,

or,

There are then off-diagonal elements, so there are subsets of the off-diagonal pairs.

I can combine any of these subsets with the diagonal to get a reflexive relation on A.

All in all, reflexive relations..

Is this a good way to think of the reflexive property, or am I way off?

Thanks!