The accurate hierarchy of number sets within the real number system, from largest to smallest, is:
rational numbers, integers, whole numbers, natural numbers
This is because:
- Rational numbers include all integers and fractions (which can be expressed as ratios).
- Integers are whole numbers that can be positive, negative, or zero.
- Whole numbers are non-negative integers (0, 1, 2, 3, ...).
- Natural numbers are the positive integers (1, 2, 3, ...).
Thus, the complete accurate response is: rational numbers, integers, whole numbers, natural numbers.