The set of numbers that are real numbers but cannot be expressed as one integer divided by another are called irrational numbers.
Irrational numbers cannot be written as a fraction \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0\). Examples of irrational numbers include \( \sqrt{2} \), \( \pi \), and \( e \).