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."
Read more about Abuse Of Notation: Examples, Bourbaki, Abuse of Language or Notation?
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