Law (mathematics)

Statement

In mathematics, a law is a formula that is always true within a given context. Laws describe a relationship, between two or more expressions or terms (which may contain variables), usually using equality or inequality, or between formulas themselves, for instance, in mathematical logic. For example, the formula $a^2 \geq 0$ is true for all real numbers $a$, and is therefore a law. Laws over an equality are called identities. For example, $(a+b)^2 = a^2 + 2ab + b^2$ and $\cos^2\theta + \sin^2\theta =1$ are identities. Mathematical laws are distinguished from scientific laws which are based on observations, and try to describe or predict a range of natural phenomena.