Let’s consider the partial order relation.

Namely, it’s a relation that has the following properties: reflexive, transitive, antisymmetric.

One example of such a relation is ≤ on naturals.

Another example is ⊆ on sets.

But if we look at these 2 examples from a higher perspective, the first one is about comparing numbers and the second one is about subsets of a set. E.g. 1 ≤ 2 and {1, 2} ⊆ {1, 2, 3}

It might not be immediately obvious that these 2 examples have anything in common, but with partial orders (and algebraic structures in general) we can capture such abstractions.

Advertisements