Question

Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?(1 point) Responses irrational numbers, square roots, endless decimals, pi, natural numbers, whole numbers, integers, rational numbers, integers, rational numbers, natural numbers, whole numbers, rational numbers, integers, whole numbers, natural numbers

Answer 1

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

1. Real Numbers (includes both rational and irrational numbers)
   • Rational Numbers (numbers that can be expressed as a fraction; includes integers and whole numbers)
     • Integers (whole numbers and their negatives)
       • Whole Numbers (non-negative integers, including zero)
         • Natural Numbers (positive integers, counting numbers, starting from 1)
   • Irrational Numbers (numbers that cannot be expressed as fractions; includes square roots of non-perfect squares, endless decimals like π)

So, from largest to smallest, the hierarchy is:

1. Real Numbers
2. Rational Numbers
3. Irrational Numbers
4. Integers
5. Whole Numbers
6. Natural Numbers

If you were to include specific examples like "pi," "endless decimals," or "square roots," you would reference the sets they belong to when explaining their hierarchy.

In a simplified form, an appropriate listing might look like this:

1. Real Numbers
2. Rational Numbers
3. Irrational Numbers
4. (Numbers like Pi, Square Roots)
5. Integers
6. Whole Numbers
7. Natural Numbers

Therefore, if you need the direct list you provided packaged more correctly, it might look like this:

Rational Numbers, Irrational Numbers, Integers, Whole Numbers, Natural Numbers.

Keep in mind that irrational numbers are a separate group that is generally more challenging to define. If your task is strictly about the integers, whole numbers, and natural numbers, then the latter three can also be arranged accordingly. However, they all fall under the umbrella of the real number system.