The set of numbers that are real numbers but cannot be expressed as one integer divided by another is described as irrational numbers.
Irrational numbers are numbers that cannot be expressed as a fraction of two integers (i.e., they cannot be written in the form \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \)). Examples include numbers like \( \sqrt{2} \), \( \pi \), and \( e \).
On the other hand, rational numbers can be expressed as one integer divided by another. Therefore, the correct answer is irrational.