equality (mathematics)

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between A and B is written A = B, and pronounced A equals B. The symbol "=" is called an "equals sign". Thus there are three kinds of equality, which are formalized in different ways.

• Two symbols refer to the same object.
• Two sets have the same elements.
• Two expressions evaluate to the same value, such as a number, vector, function or set.

These may be thought of as the logical, set-theoretic and algebraic concepts of equality respectively.