👉 Mathematical violations refer to situations where the principles, rules, or assumptions underlying a mathematical theory or problem are not properly followed, leading to incorrect conclusions or results. These violations can stem from several sources, such as applying the wrong mathematical operation, ignoring fundamental axioms, using undefined or inconsistent definitions, or misinterpreting theorems and their conditions. For example, dividing by zero is undefined in standard arithmetic, violating the principle that division should always result in a well-defined number. Similarly, failing to satisfy the axioms of set theory or the rules of logical inference can lead to paradoxes or invalid theorems, undermining the integrity of mathematical reasoning.
