Yes, both rational numbers and irrational numbers are included in the set of real numbers.
To clarify, rational numbers are those that can be expressed as the quotient of two integers, where the denominator is not zero. Examples of rational numbers include 1/2, -3, and 0.75.
On the other hand, irrational numbers cannot be expressed as a simple fraction. They are non-repeating and non-terminating decimals. Classic examples of irrational numbers are π (pi) and √2 (the square root of 2).
Both rational and irrational numbers together make up the complete set of real numbers, which can be visualized on a number line. This inclusion is crucial because real numbers are used in various fields of mathematics and apply to many real-world situations.