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Multivalued functionIn mathematics, a multivalued function is a total relation; i.e. every input is associated with one or more outputs. Strictly speaking, a "well-defined" function associates one, and only one, output to to any particular input. The term "multivalued function" is, technically, a logical contradiction, "true" functions are monovalued.
The above diagram does not represent a "true" function; because, the element 3, in X, is associated with two elements b and c, in Y. See also: 
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Multivalued function".