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,...

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

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