document.write( "Question 395724: Why is the set of odd numbers equivalent to the set of whole numbers? \n" ); document.write( "

Algebra.Com's Answer #280858 by richard1234(7193) $\"\"$ $\"About$

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It's because there exists a bijective function that maps the odd numbers to the set of whole numbers.\r
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\n" ); document.write( "\n" ); document.write( "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 $\"abs%28A%29+=+abs%28B%29\"$ . \n" ); document.write( "

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