Which list shows an accurate HIERARCHY numbers said within the real number system from largest to smallest

Answer 1

In the real number system, the hierarchy from largest to smallest can generally be represented as follows:

1. Real Numbers (ℝ)

   • Includes all rational and irrational numbers.

2. Rational Numbers (ℚ)

   • Numbers that can be expressed as a fraction of two integers (e.g., 1/2, -3, 0.75).

3. Irrational Numbers

   • Numbers that cannot be expressed as a simple fraction (e.g., π, √2).

4. Integers (ℤ)

   • Whole numbers that can be positive, negative, or zero (e.g., -3, 0, 1).

5. Whole Numbers

   • Non-negative integers (e.g., 0, 1, 2, ...).

6. Natural Numbers (ℕ)

   • Positive integers (e.g., 1, 2, 3, ...).

In a more simplified order focusing solely on the broadest categories, it can be expressed as follows:

• Real Numbers (ℝ)
  • Rational Numbers (ℚ)
  • Irrational Numbers
  • Integers (ℤ)
  • Whole Numbers
  • Natural Numbers (ℕ)

Keep in mind that within these categories, individual numbers can be compared directly (e.g., 3 is larger than 2, and -1 is less than 0), but this list organizes categories rather than individual values.