Order Relation

Order Relation

Relation of inequality between two quantities with different values.

Binary relation in a set that allows us to compare its elements to one another in a coherent way.


  • A set equipped with an order relation is an ordered set.
    It is also said that the relation defines an order structure or simply an order on this set.
  • An order relation in a set E is a relation that is both antisymmetric and transitive.


  • The symbol “<” is read as: “is less than“.
  • The symbol “>” is read as: “is greater than“.

These two relations of inequality can be translated in different ways:

  • 3 comes before 5
  • 5 comes after 3
  • 3 is the predecessor of 4
  • 6 is the successor of 5
  • 4 comes immediately before 5
  • 4 comes immediately after 3
  • 4 is located between 3 and 5


  • The relation 3 < 5 is read as: “three is less than five”.
  • The relation 5 > 3 is read as: “five is greater than three”.

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