

Function (mathematics)  Wikipedia, the free encyclopedia 
  Thus, the "is a square root of" relation is a function, and it contains for example, the pairs (3, 9) and (3, 9); while the converse, "is the square of" relation, is not a function because it contains both the pairs (9, 3) and (9, −3), and 3 is not equal to −3. 
  In this definition, a function is a special case of a relation, in particular a function is a relation in which every first element has a unique second element. 
  The number of computable functions from integers to integers is countable, because the number of possible algorithms is. The number of all functions from integers to integers is higher: the same as the cardinality of the real numbers. 
 en.wikipedia.org /wiki/Mathematical_function (3457 words) 
