Does a strict partial order relation have to be antisymmetric or asymmetric?

Question

Mathematics

Hello!
Tell me, please, a strict partial order relation should have the property of antisymmetry (skew-symmetric) or asymmetry ? In many articles it is written that - antisymmetric . Although, by definition, asymmetric is more suitable .

Answer 1

There is no contradiction. Both at the same time.
https://en.wikipedia.org/wiki/Order_relation#St...

If the condition of reflexivity is replaced by the condition of anti-reflexivity...
then we obtain the definition of a strict or anti-reflexive partial order...
Remark. The simultaneous antireflexivity and transitivity of a relation implies asymmetry , which is a stronger condition than antisymmetry .