Abuse of notation

In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help to simplify the exposition or to suggest the correct intuition, while possibly minimizing errors and confusion at the same time.

A closely related concept is abuse of language or abuse of terminology, where a term — rather than a notation — is used informally. 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 itself a "representation of G."

Since both mathematical notation and terminology vary across time and context, what is flagged as abuse in one context could be formally correct in another. Furthermore, abuse of notation should not be conflated with misuse of notation, which does not have the presentational benefits of the former and should be avoided, such as the misuse of constants of integration.

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