Editing Closure
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A Set is closed under a binary operation if any two elements of the set when combined using the binary operation produce an element of the same set. Thus a set A is closed under the binary operation * if for all a and b EQN:\in\ A then a * b EQN:\in\ A. This idea extends beyond simple binary operations. For example: * The set of natural numbers is closed under addition and multiplication ** but not closed under subtraction. * The set of the integers is closed under addition, subtraction and multiplication ** but not under division Some counter-examples: * The set of rational numbers is not closed under minimum upper bound * The set of real numbers is not closed under square roots