I have some confusion about the definition of maximum elements. On the wikipedia page it says this:
Formally, given a partially ordered set (P, ≤), an element g of a subset S of P is the greatest element of S if s ≤ g, for all elements s of S.
My question is: Why is the ≤ sign not a < sign? As I understand, a maximum element is unique within a poset (partially ordered set). It seems more logical to me that a < sign would be used instead of a ≤ sign, to ensure that the maximum is unique.
Is it because of the fact that in this poset (P, ≤) only the ≤ sign is relevant and that the < sign is not at play?