Definition

1. Adjective:
   • Unchanged in value following multiplication by itself: In mathematics and computer science, an operation or element is described as "idempotent" if applying it multiple times yields the same result as applying it once. For example, multiplying a number by 1 is idempotent because 1 × 1 = 1.

Usage Examples

• Adjective:
  • In programming, the HTTP method PUT is often designed to be idempotent.
  • The identity matrix is idempotent because when you multiply it by itself, you get the same matrix.
  • Setting a variable to a specific value is an idempotent operation.

Advanced Usage

• Idempotence in Computing: A key concept in designing reliable systems, especially for network operations and APIs. An idempotent request can be safely repeated without causing unintended side effects.

  • Making an API call idempotent prevents duplicate transactions if a request is sent multiple times due to network issues.

• Idempotent Element in Algebra: An element in a set (like a matrix or a function) that, when combined with itself under a given operation (like multiplication or function composition), yields itself.

  • The zero function under composition is idempotent because f(f(x)) = f(x).

Variants and Related Words

• Idempotence (noun): The property of being idempotent.
  • The idempotence of the operation guarantees consistency.

Synonyms

• Nullipotent (in specific contexts, though this often means an operation that has no effect, which is a form of idempotence).
• Self-identical under the operation (a descriptive phrase).

Antonyms

• Non-idempotent: Not having the idempotent property.
  • The POST method is typically non-idempotent as it may create a new resource each time it is called.

Related Phrases and Concepts

• Idempotent Law: A law in Boolean algebra and set theory stating that an element combined with itself is equal to itself (e.g., A ∪ A = A, A ∩ A = A).
• Idempotent Semigroup: A mathematical structure where every element is idempotent.

Adjective

1. unchanged in value following multiplication by itself
   • this matrix is idempotent