I'm studying the properties of relations. I'm struggling in getting the point for the following exercise:
Let $R$ be the relation "is strictly higher than" applied to the set of all mountain peaks. The exercise asks whether this relation is antisymmetric. The correct answer is that it is.
I understand that a relation is antisymmetric if:\begin{equation}x \ R \ y \ \ \text{and} \ \ y \ R \ x \implies x = y\end{equation}Now, if mountain A is strictly higher than mountain B, then mountain B can never be higher than mountain A. So this condition can never happen. I don't get why $x = y$.Can you give me some intuition?