Inductive set (axiom of infinity)

In the context of the axiom of infinity, an inductive set (also known as a successor set) is a set with the property that, for every , the successor of is also an element of and the set X contains the empty set .

More formally, X is inductive if

An example of an inductive set is the set of natural numbers.

See also

• Natural number
• Peano axioms

External links

• Mathworld: Inductive set

References

• Hrbacek, Karel; Jech, Thomas (1999). Introduction to Set Theory (3 ed.). Marcel Dekker. ISBN 0824779150. 

This article incorporates material from inductive set on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.