##  [Idempotent Law](/index.php/idempotent-law) 

  ##  [Idempotent Law](https://mathlogic.quantumdictionary.io/idempotent-law-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/index.php/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The law that applying the same binary idempotent operator to identical operands yields the same operand: for a connective ⊗ that is idempotent, A ⊗ A = A (examples: A ∧ A = A, A ∨ A = A; likewise set union A ∪ A = A).

 

 

 

 

 





 

 



 ##  [Idempotent Law](https://algebra.quantumdictionary.io/idempotent-law-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The property of an operation or element such that applying the operation multiple times has the same effect as applying it once. For a binary operation written ·, idempotence means x·x = x for all x (or for a specific element x). For unary operations f, idempotence is f(f(x)) = f(x).