idempotenssia

Idempotence is a property of an operation or function whereby applying it multiple times yields the same result as applying it once. In mathematics, an element e in a semigroup with operation ⋅ is idempotent if e ⋅ e = e. In computer science, a function f: X → X is idempotent if, for all x in X, f(f(x)) = f(x).

Common algebraic examples include projection operations: applying a projection twice yields the same result as applying it once. In Boolean algebra, x ∧ x = x and x ∨ x = x; in set theory, A ∩ A = A and A ∪ A = A. Under standard multiplication, a number a satisfies a^2 = a only for a = 0 or a = 1, so most numbers are not idempotent under multiplication.

In computing, idempotence is important for reliability and repeatability. An idempotent operation can be retried without causing additional effects. In web services and APIs, certain HTTP methods are designed to be idempotent: GET reads a resource without changing state, PUT and DELETE are intended to produce the same effect on repeated requests, and POST is typically non-idempotent because it usually creates new resources. Real-world implementations may vary, but the intention is to minimize unintended side effects from retries.

Practical use includes designing APIs and distributed systems to be idempotent through stable identifiers, upserts, conditional requests, and idempotency keys that allow duplicates to be detected and discarded. Idempotence helps ensure correctness in failure scenarios, improves reliability, and simplifies reasoning about repeated operations.