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

In the real number system, the hierarchy of number sets from largest to smallest is as follows:

1. **Real Numbers (ℝ)** - This includes all rational and irrational numbers.
- Example: All integers, fractions, and irrational numbers like √2, π.

2. **Rational Numbers (ℚ)** - This includes all numbers that can be expressed as a fraction of two integers (where the denominator is not zero).
- Example: 1/2, 3.75, -1 (which can be expressed as -1/1).

3. **Irrational Numbers** - This is a subset of real numbers that cannot be expressed as a simple fraction. They cannot be written as the ratio of two integers.
- Example: √2, π, e.

4. **Integers (ℤ)** - This includes whole numbers and their negatives.
- Example: -3, 0, 2.

5. **Whole Numbers** - This is a subset of integers that includes all non-negative integers.
- Example: 0, 1, 2, 3, ...

6. **Natural Numbers (ℕ)** - This includes the positive integers, often starting from 1.
- Example: 1, 2, 3, ...

So, a complete hierarchy from largest to smallest would be:

**Real Numbers (ℝ) > Rational Numbers (ℚ) > Irrational Numbers > Integers (ℤ) > Whole Numbers > Natural Numbers (ℕ).**