##  [Well-Ordering Principle](/well-ordering-principle) 

  ##  [Well-Ordering Principle](https://algebra.quantumdictionary.io/well-ordering-principle-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The claim that every nonempty set of positive integers (or more generally every set that is well-orderable) has a least element with respect to the usual ordering; in practice often stated for the natural numbers as 'every nonempty subset of N has a least element.'