Well Ordered Set - kipawaa/Proof-Tree GitHub Wiki

Statement

A set $(A, \leq)$ is a well-ordered set iff $\leq$ is a Linear Ordering of $A$ and every non-empty Subset of $A$ has a Least Element.

Explanation

Proof(s)

History

Applications

Links

Dependencies

• Subset
• Linear Ordering
• Least Element

Dependents

• 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