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:
- equivalence relations (The definition of order relations parallels that of equivalence relations.)
- 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
→ Elements of Set Theory
An introductory textbook on axiomatic set theory.
- Chapter 3, "Relations and functions," subsection "Ordering relations," pages 62-64
- Chapter 7, "Orderings and ordinals," subsection "Partial orderings," pages 167-172
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