Order relations?

Hello, is "=" a partial order relation?
For example, there is a set a = {1, 2}. Then the Cartesian product A x A = { (1; 1), (2; 2), (1; 2), (2; 1) }.
Therefore R = { (1; 1), (2; 2) }, if R = "=".
Then it turns out that R is a partial order relation since it is reflexive, antisymmetric and transitive. But R is not relations of linear order. In fact ∃ a, b ∈ A !(=>) aRb v bRa.
As I understand it, partial order does not require that every element of a set are pairwise in relation with other elements of the set. On this basis, can we call the set A is a partially ordered? Because the set R is set to a partial order.
April 4th 20 at 13:05
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