Provide two different functions and show how to use each of

Provide two different functions and show how to use each of the functions to prove the set is infinite:

\"The set of all natural numbers is an infinite set.\"

Solution

For example,

        the set of natural numbers N = {1, 2, 3, ... } can be paired with the set of odd numbers E = {1, 3, 5, ... } by the  function f(n) = 2n+1

and second example,

        if f(y) = y / (1 + |y|) pairing R with the interval (-1, 1). Thus, R ~ (-1, 1), which shows that R is an infinite set.