Science:Math Exam Resources/Courses/MATH220/December 2011/Question 05 (a)/Solution 1
A set A is denumerable if it is in bijective correspondence with the natural numbers. That is, it is denumerable if and only if there exists a bijective function
Note: Mathematicians think of this function as a counting of all the elements of the set A. Given a counting, that is such a bijection ƒ the first element of the set A is the one that is mapped to 1 by the function, the second element is the one mapped to 2 and so on. Observe that we need to require the function to be bijective to guarantee that all the elements are counted and are counted in a unique way (we don't want to have two elements mapped to the same natural number).