Consistency in mathematics

In mathematics, consistency refers to the idea that a set of statements or axioms do not lead to any contradictions. This means that if a mathematical system is consistent, you cannot derive both a statement and its opposite from the same set of rules. For example, in a consistent system, you cannot prove that 2 + 2 equals 4 and also prove that 2 + 2 equals 5. Consistency is crucial because it ensures the reliability and validity of mathematical reasoning, allowing mathematicians to build upon established truths without running into logical conflicts.