---
tag: WFNYQEWM4X
kind: concept
name: Simply infinite set
sources:
  - wikipedia: en:43580500@r1360947732
    locator: Glossary of set theory, section S
    note: adopted
    mention: wikipedia://en/43580500#WDO8
    sections: [Summary]
inventory: [ZZN4Y1XVNM]
---

## Summary

A term sometimes used for [[infinite sets|01MKW4R283]], i.e., sets equinumerous with N, to contrast them with Dedekind-infinite sets. In ZF, it can be proved that all Dedekind-infinite sets are simply infinite, but the converse – that all simply infinite sets are Dedekind-infinite – can only be proved in ZFC.