Inductive Set

Statement

A set $I$ is inductive iff $\emptyset \in I$ and $x \in I \implies S(x) \in I$, i.e. if it contains the Empty Set and the Successor of any element is also in the set.

Explanation

Proof(s)

History

Applications

Links

Dependencies

• Successor
• Empty Set

Dependents

• Axiom of Infinity

Sources

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