Mathematical equivalence refers to the relationship between two expressions or statements that have the same value or meaning. For example, the equations 2 + 3 and 5 are mathematically equivalent because they represent the same quantity. This concept is essential in mathematics, as it allows for the simplification and manipulation of expressions without changing their inherent value. In logic, mathematical equivalence can also apply to statements that yield the same truth value. For instance, the statements p and not not p are equivalent because they are both true or both false under the same conditions. Understanding equivalence helps in solving problems and proving theorems in various branches of mathematics.