SOLUTION: Why is the set of odd numbers equivalent to the set of whole numbers?

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Question 395724: Why is the set of odd numbers equivalent to the set of whole numbers?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
It's because there exists a bijective function that maps the odd numbers to the set of whole numbers.

If A = {...-5, -3, -1, 1, 3, 5...} and B = {0, 1, 2, 3, ...} then if we let f%28x%29+=+abs%28x%29 for all x contained in A, we get the set {1, 1, 3, 3, 5, 5, ...} (after reordering). Subtracting one from every other term starting with the first term we get {0, 1, 2, 3, ...}, or B. Therefore the two sets have the same cardinality, or abs%28A%29+=+abs%28B%29.