Self‐Inclusion Property - kipawaa/Proof-Tree GitHub Wiki

Statement

Every set is a subset of itself, i.e. for any set $A, A \subseteq A$.

Explanation

Proof(s)

By definition of $A$, forall $x$, if $x \in A$ then $x \in A$.
Hence by definition of Subset, $A \subseteq A$.

History

Applications

Links

Dependencies

• Subset

Dependents

Sources

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