Law (mathematics)

In mathematics, a law is a formula that is always true within a given context.^[1] Laws describe a relationship, between two or more expressions or terms (which may contain variables), usually using equality or inequality,^[2] or between formulas themselves, for instance, in mathematical logic. For example, the formula ${\displaystyle a^{2}\geq 0}$ is true for all real numbers a, and is therefore a law. Laws over an equality are called identities.^[3] For example, ${\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}$ and ${\displaystyle \cos ^{2}\theta +\sin ^{2}\theta =1}$ are identities.^[4] Mathematical laws are distinguished from scientific laws which are based on observations, and try to describe or predict a range of natural phenomena.^[5] The more significant laws are often called theorems.