Consider an arbitrary set equipped with a strict order $(X,<)$ such that we have:
$$\forall a,b\in X\left(a\neq b\implies (a<b)\lor (a>b)\right)$$
I frequently see this relation being called a "strict total order" yet the term itself is an oxymoron. For in order for a relation to be total it must be reflexive which would contradict it being a strict order.
Also while on the topic, I would be grateful if someone could explain to me why in order theory there is a focus on partial orders rather then strict orders.
Now I understand any work on partial orders can be transplanted over to give analogous theorems on strict orders, in the same way elementary theorems in linear algebra regarding the rows of a matrix can analogously be translated into theorems on the columns of a matrix. Thus making the distinction between whether we choose strict or partial orders somewhat trivial. However the concept of a strict order seem a bit more intuitive at least when viewing finite posets, for instance the nodes/vertices in a hasse diagram could be viewed as the directed acyclic graphs formed by the covering relations of a strict order.