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, whole numbers, and fractions.
- Integers include whole numbers and their negative counterparts.
- Whole numbers include natural numbers and zero.
- Natural numbers are the counting numbers (1, 2, 3, ...).
So, the correct response is:
rational numbers, integers, whole numbers, natural numbers.