---
tag: VANEC1ZGAA
kind: concept
name: Inductive
sources:
  - wikipedia: en:43580500@r1360947732
    locator: Glossary of set theory, section I
    note: adopted
    mention: wikipedia://en/43580500#32ML
    sections: [Summary]
inventory: [6SK74SZ1N1]
---

## Summary

An inductive set is a set that can be generated from a base set by repeatedly applying a certain operation, such as the set of natural numbers generated from the number 0 by the successor operation.

An inductive definition is a definition that specifies how to construct members of a set based on members already known to be in the set, often used for defining recursively defined sequences, functions, and structures.

A poset is called inductive if every non-empty ordered subset has an upper bound