nietidempotent

Niet-idempotent, more commonly referred to as non-idempotent, describes an operation or process where applying it more than once yields a different result from applying it once. An operation f is idempotent if, for every input x, f(f(x)) = f(x). If this equality fails for some x, the operation is non-idempotent.

In mathematics, non-idempotent examples are common. For instance, f(x) = x + 1 is non-idempotent since f(f(x)) = x + 2, which is not equal to f(x). By contrast, idempotent examples include f(x) = |x| or f(x) = max(x, 0), where applying the function again does not change the result beyond the first application.

In computer science and software engineering, idempotence is a desirable property for certain operations, particularly those that can be retried safely. Non-idempotent operations include many write actions that accumulate state, such as creating a new resource with an HTTP POST or incrementing a counter. Because repeated executions produce additional side effects, non-idempotent operations require careful handling in distributed systems, such as using unique identifiers, tokens, or compensating actions to prevent unintended duplication.

In mathematical structures, idempotence is defined for elements or morphisms by the rule e ∘ e = e. Non-idempotent elements or morphisms do not satisfy this condition, reflecting that repeated application changes the result.

Overall, identifying whether an operation is non-idempotent helps inform retry strategies, state management, and system design choices to avoid unintended consequences.