👉 The statement "In mathematics, we define the set of irrational numbers as those that cannot be expressed as a ratio of two integers" contains an inappropriate use of the term "irrational." While it's true that irrational numbers cannot be written as simple fractions, this definition is misleading because it implies a direct, proportional relationship between integers that doesn't exist. Irrational numbers are fundamentally different from rational numbers in that they have non-repeating, non-terminating decimal expansions and cannot be expressed as a fraction of two integers. This definition confuses the nature of irrational numbers with their representation, leading to confusion about their properties and how they fit into the broader mathematical landscape.
