In Exercises, we give an expression describing the number that corresponds to the natural...

In Exercises, we give an expression describing the number that corresponds to the natural number a Use this expression to describe a one-to-one correspondence between the natural numbers and one of its subsets. For example, if we gave you the expression 2n, you would write the following correspondence that we gave in Example:

3n

The Set of Natural Numbers Is Infinite

Show that the set of natural numbers is infinite.

SOLUTION:

Let N = {1, 2, 3, …;} and E = {2, 4, 6, …;}, then the following is a one-to-one correspondence between N and its proper subset E:

1  2  3 …; n …;

↕  ↕  ↕      ↕

2  4  6 …; 2n …;