Idempotent Law

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).

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).