The correct 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 fractions and integers, so they are the largest set.
- Integers include all whole numbers and their negative counterparts, so they form a subset of rational numbers.
- Whole numbers include all non-negative integers (0 and positive integers), which are a subset of integers.
- Natural numbers include all positive integers (1, 2, 3, ...), which are a subset of whole numbers.
Thus, the accurate response is:
rational numbers, integers, whole numbers, natural numbers.