identities

In mathematics, an identity is a true statement or equation that holds true for all values of the variables involved. Think of it as a reliable rule or formula, like the fact that multiplying any number by one doesn’t change it (e.g., 5 × 1 = 5). Identities help us simplify complex problems and reveal relationships between different mathematical expressions. They are foundational tools that mathematicians use to solve equations, prove theorems, and understand how different parts of math connect seamlessly.