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 numbers that can be expressed as a fraction, including integers and whole numbers.
- Integers include all whole numbers and their negatives.
- Whole numbers include all natural numbers and zero.
- Natural numbers include the positive counting numbers (1, 2, 3, ...).
Thus, the appropriate response is:
rational numbers, integers, whole numbers, natural numbers