The correct category that matches the set of whole numbers {0, 1, 2, 3, 4, ....} is:
4). Rational Ratios with a denominator ≠ 1
This is because whole numbers can be expressed as rational numbers where they have a denominator of 1 (for example, 3 can be expressed as 3/1), making them part of the category of rational numbers, including their opposites.