order relations


A relation is an order relation if it is irreflexive, asymmetric, and transitive. An order relation < is a total order if for any A and B, either A < B, B < A, or A = B; otherwise it is a partial order.


This concept has the prerequisites:


  • Define order relation
  • Know the distinction between total orders and partial orders
  • Be able to show that something is total or partial order
  • Know the distinction between maximal element and largest element

Core resources (read/watch one of the following)


Stanford CS103: Mathematical Foundations of Computing (2013)
Lecture notes for Stanford's introductory computer science theory course.
Location: Section 5.3, "Order relations," up through 5.3.3, "Hasse diagrams," pages 271-286
Author: Keith Schwarz


See also

-No Additional Notes-