Question 395724
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(x) = abs(x)}}} 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(A) = abs(B)}}}.