Identity

In mathematics, an identity is an equality that holds true for all values of the variables within its domain. It is a relationship between two mathematical expressions that are equal for all possible values of the common variables.

For example, in trigonometry, the Pythagorean identity holds for all values of .

An identity typically represents a property of the operations involved, and they are often used to simplify expressions or solve equations.

Law

In mathematics, a law refers to a universally accepted principle or rule that describes a particular mathematical relationship or property. These mathematical laws are typically proven truths, derived from axioms or basic assumptions, that hold under specific conditions.

Theorem

A theorem is a statement that has been proven to be true within the framework of a mathematical system, based on the system's axioms and previously established theorems.