Which set of numbers includes both rational and irrational numbers?

The correct answer is the set of real numbers because it encompasses all numbers that can be found on the number line, including both rational and irrational numbers. Rational numbers are those that can be expressed as a fraction of two integers, such as 1/2, 3, or -4. In contrast, irrational numbers cannot be expressed as simple fractions; examples include numbers like √2 and π, which continue infinitely without repeating.

Understanding this set is key to recognizing the broader classifications within the number system. Whole numbers, natural numbers, and integers each represent subsets of the real numbers, but they do not include irrational numbers. Whole numbers are non-negative numbers (0, 1, 2, ...), natural numbers start from 1 and are also non-negative, while integers include positive and negative whole numbers. Thus, real numbers uniquely provide the comprehensive category that incorporates the entire range of numerical types.