11. These are all examples of multivalued functions that come about from non-injective functions. 12. :: : : See Exponentiation # Roots of arbitrary complex numbers and multivalued function. 13. Often, the restriction of a multivalued function is a partial inverse of the original function. 14. The term " multivalued function " is, therefore, a misnomer because functions are single-valued. 15. Therefore, a multivalued dependency is a special case of " tuple-generating dependency ". 16. Ronald Fagin demonstrated that it is always possible to achieve 4NF . Rissanen's theorem is also applicable on multivalued dependencies. 17. 2-ary join dependencies are called multivalued dependency as a historical artifact of the fact that they were studied before the general case. 18. In complex analysis, the "'principal values "'of a multivalued function are the values along one chosen real number. 19. In contrast to the functional dependency, the "'multivalued dependency "'requires that certain tuples be present in a relation. 20. :Be careful because e ^ z is not one-to-one ( i . e . logarithm is a multivalued function ).
