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A function f is considered idempotent if f(f(x)) = x. Computer science defines a procedure idempotent if its result is the same when called repeatedly with the same arguments.
This is an especially useful property when dealing with retry of a replicated object. When a communication failure occurs while invoking a remote method, it's not always possible to know if the failure occurred before or after the method invoked was completed on the server. If the failure occurred after the method completed on the server, a retry will result in calling the same method twice (albeit on another server). Such behavior can lead to incorrect results unless the method is idempotent. In that case, invoking the same method with the same arguments multiple times is no different that invoking it once.