Show that the set of whole numbers, W. is equivalent to the set of natural numbers, N, by carefully describing a one-to-one correspondence between the sets

f (0) = 0

f (n) = 2n-1 for n = 1, 2, 3, ...

f (n) = - 2n for n = - 1, - 2, - 3, ...

Step-by-step explanation:

Since integers and natural numbers are both infinite numerable, they can be arranged in sequences

0, 1, - 1, 2, - 2, 3, - 3, 4, - 4, ...

0, 1, 2, 3, 4, 5, 6, 7, 8, ...

So the map that assigns to each integer the natural below it in the arrange showed above, is clearly a one-to-one map.

This map could be described as

f (0) = 0

f (n) = 2n-1 for n = 1, 2, 3, ...

f (n) = - 2n for n = - 1, - 2, - 3, ...