Which of the following defines an irrational number?

An irrational number is specifically defined as a real number that cannot be expressed as the ratio of two integers. This means that it cannot be represented in the form ( \frac{a}{b} ), where ( a ) and ( b ) are integers and ( b ) is not zero. Examples of irrational numbers include (\sqrt{2}), (\pi), and (e). These numbers have non-repeating, non-terminating decimal expansions, distinguishing them from rational numbers, which either terminate or repeat.

In contrast, the other options describe different categories of numbers. For instance, a number that can be expressed as a ratio of two integers accurately defines a rational number, not an irrational one. Whole numbers are non-negative integers (0, 1, 2, 3, ...), and even integers are whole numbers that can be divided by 2 without leaving a remainder. Therefore, these categories do not encompass the definition of an irrational number.