Which list shows an accurate hierarchy of numbers set within the real number system, from largest to smallest
1. Irrational numbers
2. Rational numbers
3. Integers
4. Whole numbers
5. Natural numbers
The real number system is a continuum of numbers that includes rational numbers (fractions and decimals that can be expressed as a ratio of two integers) and irrational numbers (decimals that cannot be expressed as a ratio of two integers). Within the real number system, we can organize numbers in a hierarchical order based on their relative size.
The hierarchy of numbers in the real number system from largest to smallest is as follows:
1. Positive infinity (∞) - This represents a number that is larger than any real number.
2. Positive numbers - These are numbers greater than zero.
3. Zero (0) - It is neither positive nor negative and represents the absence of quantity.
4. Negative numbers - These are numbers less than zero.
5. Negative infinity (-∞) - This represents a number that is smaller than any real number.
6. Irrational numbers - These are numbers that cannot be expressed as a fraction or a terminating or repeating decimal. They include numbers like π (pi) or √2 (square root of 2).
7. Rational numbers - These are numbers that can be expressed as a fraction or a terminating or repeating decimal. They include numbers like 1/2 or 0.75.
8. Real numbers as a whole - This includes both rational and irrational numbers merged together as a continuum.
It's important to note that the exact positioning of specific numbers within this hierarchy may vary, as there are an infinite number of numbers within each category.