ordering
Complete
Summary
Additional properties of binary relations
antisymmetric -> the only two-way relations are self-loops
totality -> every element is related to every other element in at least one way
Partial order
- a relation that is reflexive, antisymmetric and transitive
Total order
- a partial order that is total
Concept
Bounded below
Well-ordering principle for integers
- basis for proof by induction
- in a totally ordered set, that is bounded below by some integer, there is a smallest integer
Proving properties
Application
Well-ordering does not apply to all sets