Linear Ordering - kipawaa/Proof-Tree GitHub Wiki

Statement

An Ordering $\leq$ on a set $S$ is a linear order (sometimes called a total order) iff $\forall a, b \in A, a$ and $b$ are Comparable.

Explanation

Proof(s)

History

Applications

Links

Dependencies

• Partial Ordering
• Comparable

Dependents

• Well Ordered Set
• Linearly Ordered Set
• Ordinals Are Closed Under Succession

Sources

• Hrbacek, K., & Jech, T. (1999). Introduction to Set Theory, Revised and Expanded (3rd ed.). CRC Press. https://doi.org/10.1201/9781315274096