exactly one element
[exactly one element|exactly one element] A function is a relation that assigns to each element in its domain exactly one element in the range.
Definition
exactly one element A function is a relation that assigns to each element in its domain exactly one element in the range. For example, the relation pairing first five natural numbers with their doubles is a function because each domain element maps to exactly one range element.
Mechanism
exactly one element The relation pairs each domain element { 1 , 2 , 3 , 4 , 5 } with exactly one range element { 2 , 4 , 6 , 8 , 10 } , demonstrating a function as defined by assigning unique range elements to domain elements.
Examples
exactly one element The relation pairs each of the first five natural numbers with exactly one element in the range { 2 , 4 , 6 , 8 , 10 } , demonstrating a function where each domain element is mapped to a unique range value.