##  [Order](/order) 

  ##  [Order](https://algebra.quantumdictionary.io/order-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For an element in an algebraic structure with a binary operation and a neutral element, the order is the smallest positive integer n such that applying the operation to the element with itself n times yields the neutral element; if no such n exists the element is said to have infinite order.