In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not formally correct but that seems likely to simplify the exposition or suggest the correct intuition (while being unlikely to introduce errors or cause confusion). Abuse of notation should be contrasted with misuse of notation, which should be avoided. A related concept is abuse of language or abuse of terminology, when not notation but a term is misused.
The new use may achieve clarity in the new area in an unexpected way, but it may borrow arguments from the old area that do not carry over, creating a false analogy.
Abuse of language is an almost synonymous expression that is usually used for non-notational abuses. For example, while the word representation properly designates a group homomorphism from a group G to GL(V) where V is a vector space, it is common to call V "a representation of G."
Other articles related to "abuse of notation, abuse of":
... The terms "abuse of language" and "abuse of notation" depend on context ... Writing "f A → B" for a partial function from A to B is almost always an abuse of notation, but not in a category theoretic context, where f can be seen ...
Famous quotes containing the words abuse of and/or abuse:
“Liberty is the air that we Americans breathe. Our Government is based on the belief that a people can be both strong and free. That civilized men need no restraint but that imposed by themselves against the abuse of freedom.”
—Franklin D. Roosevelt (18821945)
“Hence, the less government we have, the better,the fewer laws, and the less confided power. The antidote to this abuse of formal Government, is, the influence of private character, the growth of the Individual; the appearance of the principal to supersede the proxy; the appearance of the wise man, of whom the existing government, is, it must be owned, but a shabby imitation.”
—Ralph Waldo Emerson (18031882)