👉 The fundamental rule of mathematics, often referred to as the Law of Excluded Middle, states that for any proposition \( P \), either \( P \) is true or its negation \( \neg P \) is true. This principle underpins classical logic and ensures that every statement has a definite truth value, either affirmative or negative. In mathematical proofs, this means that if a statement cannot be proven false, it must be true, and vice versa. This binary nature of truth is crucial for the structure and validity of mathematical arguments, allowing for clear and definitive conclusions.
