---
tag: XP1SPF2VC1
kind: statement
role: proposition
name: Law (mathematics)
aliases: [law-of-mathematics]
sources:
  - wikipedia: en:77662984@r1362840840
    locator: Law (mathematics)
    note: adopted
    mention: wikipedia://en/77662984
    sections: [Statement]
same_as:
  wikidata: Q130223644
  wikipedia: Law (mathematics)
inventory: [Y4S9WYJ0J2]
---

## 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|08J2M1JYAG]] *$a$*, 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.