I think this is an informal presentation of a subject which should only be presented formally. There's already a page called Asymptotic Notation for this topic.
Yes, that's correct. I wonder if it is even a good idea to talk about transitive sets in the transitive relation page, as most people who are interested in transitive relations are not likely to care about transitive sets. When this page is expanded beyond stub status, I hope that it will focus mostly on transitivity, rather than related concepts such transitive sets, posets, and preorders.
There is a page for linearly ordered set. It is called "totally ordered set". This is one of those situations where it would be nice for arbital to have a synonym system.
I think this is an informal presentation of a subject which should only be presented formally. There's already a page called Asymptotic Notation for this topic.