Which list shows an accurate hierarchy of numbers sets in the real number system from largest to smallest natural numbers whole numbers integrators rational numbers integers rational numbers natural numbers whole numbers rational numbers integers whole numbers natural numbers internal numbers square roots endless decimals pi
The accurate hierarchy of number sets in the real number system from largest to smallest is as follows:
1) Real numbers
2) Irrational numbers (including numbers such as square roots, endless decimals, and pi)
3) Rational numbers
4) Integers
5) Whole numbers
6) Natural numbers
An accurate hierarchy of number sets in the real number system from largest to smallest would be:
- Real numbers (includes all numbers: integers, fractions, irrational numbers, etc.)
- Rational numbers (can be expressed as the ratio of two integers, e.g., 1/2, 3/4, etc.)
- Integers (includes positive and negative whole numbers, as well as zero)
- Whole numbers (includes positive integers and zero)
- Natural numbers (also known as counting numbers, includes positive integers)
The following items from your list can fit into this hierarchy:
- Real numbers [top of the hierarchy]
- Rational numbers
- Integers
- Whole numbers
- Natural numbers
Items like "internal numbers," "square roots," "endless decimals," and "pi" could fall under different subsets of real numbers, such as irrational numbers, but cannot be accurately placed in this hierarchy.
To create an accurate hierarchy of number sets in the real number system from largest to smallest, we need to understand the properties of each set and how they relate to each other.
1. Largest Set: Real Numbers (R)
The real number system encompasses all possible numbers, including rational and irrational numbers. This set includes positive and negative numbers, fractions, decimals, integers, and whole numbers.
2. Rational Numbers (Q)
Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. This set includes integers, fractions, decimals (both terminating and repeating), and whole numbers.
3. Integers (Z)
Integers are whole numbers, both positive and negative, including zero.
4. Whole Numbers (W)
Whole numbers are non-negative integers, including zero.
5. Natural Numbers (N)
Natural numbers, or counting numbers, are positive integers starting from 1 and extending infinitely.
6. Smallest Set: Other Number Representations
This category includes internal numbers, square roots, endless decimals, and irrational numbers like pi. These numbers do not fit into any of the previous sets and have unique representations.
Based on this hierarchy, the accurate list from largest to smallest would be:
Real Numbers (R)
Rational Numbers (Q)
Integers (Z)
Whole Numbers (W)
Natural Numbers (N)
Other Number Representations (Internal Numbers, Square Roots, Endless Decimals, Pi)