Which list shows an accurate hierarchy of numbers sets within the real number system, from largest to smallest?
A. Integers, rational numbers,natural numbers, whole numbers
B. Irrational numbers, square roots, endless decimals
C. Natural numbers,whole numbers,integers, rational numbers
D. Rational numbers, integers,whole numbers, natural numbers
D. Rational numbers, integers, whole numbers, natural numbers
The correct answer is:
C. Natural numbers, whole numbers, integers, rational numbers
The hierarchy of number sets within the real number system, from largest to smallest, is as follows:
1. Natural numbers: This set includes all positive whole numbers (1, 2, 3, ...), but does not include zero or negative numbers.
2. Whole numbers: This set includes all natural numbers (0, 1, 2, 3, ...), but also includes zero.
3. Integers: This set includes all whole numbers (..., -3, -2, -1, 0, 1, 2, 3, ...), including both positive and negative numbers.
4. Rational numbers: This set includes all numbers that can be expressed as a fraction (or ratio) of two integers. This includes integers as well as numbers with decimal representations that either terminate (example: 0.5) or repeat (example: 0.333...).
So, the correct order is C. Natural numbers, whole numbers, integers, rational numbers.