Addition of Equations . Such an expression is usually called an identity . The equality symbol plays a very special role in the whole of science and not only in mathematics. The notion of equality is probably more universal and basic than any other in the human thesaurus. Topologically, shapes are equal when they can be continuously transformed into one another.
Functions are equal when they take on the same values for every point they are defined on.
Sets are equal when they contain exactly the same elements. In every example the criteria of equality is different for different kinds of objects. However, the basic properties of equality do not depend on a particular family of objects being equated. Euclid's Elements , an absolutely unique book written more than 2300 years ago and that since underwent more than 2000 editions, includes the notion of equality and formulates its properties among the Common Notions . If equals be added to equals, the wholes are equal.