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 see that there is a description of double scaling above. I assume that this is what "the product rule" refers to, but it is never explicitly labeled as such. Maybe giving the paragraph above Reverse a bold heading titled "The Product Rule" would help with this.

I think it's confusing to introduce multi-argument functions before talking about currying. This makes it seem as though multi-argument functions are an intrinsic part of the lambda calculus, rather than just functions that return other functions.

There is already a page about this topic, Join and meet.

I suspect that this is going to be too fast-paced for beginners. They are going to need multiple examples and exercises for each of the concepts introduced.

This is sentence is kind of confusing. It seems like it's trying to say that if we know A = B, then we can substitute A for B (or vice versa) and get.... A = B?

It seems like it should say that if A = B, and A occurs in some equation, then we can substitute B in for A in that equation, and the resulting equation will hold.

This relies on a principle "other way" introduces but, in my opinion, is not explicit enough about: $\frac{n}{m}=n\times \frac{1}{m}$. Could this be made more explicit at the end of the "other way" section? e.g. "What we've really shown here is that $\frac{n}{m}=n\times \frac{1}{m}$".

I think that every metric space is dense in itself. If X is a metric space, then a set E is dense in X whenever every element of X is either a limit point of E or an element of E (or both).