Ordered Sets
Ordered sets are sets with an ordering.
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Description
A set does not inherently have an ordering. For some sets however, it is possible to specify one.
Consider the set of natural numbers. All members of the set can be ordered by the 'less than' binary operator (<). This is sometimes called the standard ordering for set of the natural numbers.
A set ordered by < has several properties:
∀ x,y ∈ A either x=y, x<y, or y<x
transitivity: if x<y and y<z, then x<z