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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

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Answer:

f(0) = 0

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

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

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,...

User Ron Astle Lobo
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