## You are here

Homeinductive set

## Primary tabs

# inductive set

An inductive set is a set $X$ with the property that, for every $x\in X$, the successor $x^{{\prime}}$ of $x$ is also an element of $X$.

One major example of an inductive set is the set of natural numbers $\mathbb{N}$.

Related:

NaturalNumber

Synonym:

successor set

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

03E20*no label found*45D05

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections