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numbers , is a binary operation since the sum of two natural numbers is a natural number. This is a different binary operation than the previous one since the sets are different.
* On the set of matrices with real entries, is a binary operation since the sum of two such matrices is a matrix.
* On the set of matrices with real entries, is a binary operation since the product of two such matrices is a matrix.
* For a given set , let be the set of all functions . Define by for all , the composition of the two functions

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