Which list shows an accurate hierarchy of number sets within the real number system from largest to smallest
The list that shows an accurate hierarchy of number sets within the real number system from largest to smallest is:
1. Real Numbers (R): It includes all numbers on the number line, including both rational and irrational numbers.
2. Rational Numbers (Q): It includes all numbers that can be expressed as a fraction of two integers, where the denominator is not zero.
3. Integers (Z): It includes all whole numbers (positive, negative, or zero) and their opposites.
4. Natural Numbers (N): It includes all counting numbers (positive integers) starting from 1.
5. Whole Numbers (W): It includes all non-negative integers (including zero).
The accurate hierarchy of number sets within the real number system from largest to smallest is as follows:
1. Real Numbers: This set includes all rational and irrational numbers. It is the largest set within the real number system.
2. Irrational Numbers: This set consists of numbers that cannot be expressed as fractions or decimals that terminate or repeat. Examples include √2, π, and e.
3. Rational Numbers: This set includes numbers that can be expressed as fractions or decimals that terminate or repeat. Any number that can be written as a ratio of two integers belongs to this set. Examples include 1/2, 0.75, and -3.
4. Integers: This set consists of whole numbers and their negatives, including zero. Examples include -4, -2, 0, 1, and 3.
5. Natural Numbers: This set consists of positive integers, excluding zero. Examples include 1, 2, 3, and so on.
Therefore, the hierarchy from largest to smallest within the real number system is Real Numbers > Irrational Numbers > Rational Numbers > Integers > Natural Numbers.