4
votes
1answer
84 views

Cases where reflexivity is hard to prove

A couple of remarks at Surjections and equivalence relations lead me to wonder: are there any important and/or interesting examples of reflexive relations whose reflexivity is hard to prove? There are ...
12
votes
2answers
335 views

When does “pairwise” strengthen and when does it weaken?

"Pairwise disjoint" is stronger than "disjoint"; it sometimes happens that $\displaystyle\bigcap\limits_{i\in I} A_i=\varnothing$ but for every $i,j$, or at least for some, one has $A_i \cap ...
3
votes
1answer
272 views

When is the composition of partial orders a partial order?

I have been doing some thinking about the compostition of relations and I've had trouble remembering a number of simple facts about what happens when we compose specific types of relations. I've had ...