Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?

The correct hierarchy of number sets within the real number system, from largest to smallest, is:

**Rational Numbers, Integers, Whole Numbers, Natural Numbers**

This means the correct answer is the first option.

Here's a brief explanation of each:

1. **Rational Numbers**: This set includes all fractions and integers, meaning any number that can be expressed as the ratio of two integers.
2. **Integers**: This set includes all whole numbers (both positive and negative) and zero, which are still considered rational.
3. **Whole Numbers**: This set includes all natural numbers and zero, but not negative integers.
4. **Natural Numbers**: This set includes all positive whole numbers (1, 2, 3, ...).

Thus, the hierarchy from largest to smallest is: rational numbers, integers, whole numbers, natural numbers.