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Orders
Given a set of objects, there can be numerous criteria, based on which to order them (depending on the objects themselves) — size, weight, age, alphabetical order etc.
However, currently we are not interested in the criteria that we can use to order objects, but in the nature of the relationships that define order. Of which there can be several types as well.
Mathematically, the order as a construct is represented (much like a monoid) by two components.
An order is a set of elements, together with a binary relation between the elements of the set, which obeys certain laws.
We denote the elements of our set, as usual, like this.
And the binary relation is a relation between two elements, which is often denoted with an arrow.
As for the laws, they are different depending on the type of order.
Linear order
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