Yes, it is true that no irrational numbers are whole numbers.
To understand why let’s break down the definitions: whole numbers are the set of non-negative integers, which include 0, 1, 2, 3, and so forth. On the other hand, irrational numbers are numbers that cannot be expressed as a simple fraction. This means that irrational numbers cannot be written in the form
\( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). Examples of irrational numbers include \( \sqrt{2} \), \( \pi \), and \( e \).
Since whole numbers can be expressed as fractions (for instance, 1 can be written as \( \frac{1}{1} \)), and all whole numbers are rational by definition, it follows that they cannot be irrational. The characteristics of irrational numbers fundamentally exclude them from the set of whole numbers. Therefore, the statement is indeed correct.