It's been a long time since my number theory class, but aren't there the same number of integers and odd integers? Take the set of odd integers {... -3, -1, 1,

It's been a long time since my number theory class, but aren't there the same number of integers and odd integers? Take the set of odd integers {... -3, -1, 1, 3, 5, ...} For each item, subtract one and divide the result by 2. Now you have the set of all integers without any insertions or deletions: {... -2, -1, 0, 1, 2, ...} Therefore the set of odd integers can be mapped 1:1 onto the set of all integers so they are of equal length.