Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?
A. Rational numbers, integers, whole numbers, natural number
B. irrational numbers, square roots, endless decimals, pi
C. natural numbers, whole numbers, integers, rational numbers
D. integers, rational numbers , natural numbers, whole numbers
D. integers, rational numbers, natural numbers, whole numbers
The correct answer is option C. The accurate hierarchy of number sets within the real number system, from largest to smallest is: natural numbers, whole numbers, integers, rational numbers.
Explanation:
- Natural numbers are the set of positive numbers including zero (0, 1, 2, 3, ...)
- Whole numbers include zero and all the natural numbers (0, 1, 2, 3, ...)
- Integers include all whole numbers and their negatives (... -3, -2, -1, 0, 1, 2, 3, ...)
- Rational numbers include all integers and numbers that can be expressed as fractions, where the numerator and denominator are integers and the denominator is not zero
So, the correct hierarchy is: natural numbers < whole numbers < integers < rational numbers