Abuse of notation

In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way not intended by the original inventor of the notation. This often involves modifications to the original notation.

Advantages

The new use may achieve clarity in the new area in an unexpected way.

Disadvantages

The new use may borrow arguments from the old area that do not carry over, creating a false analogy.

Examples

John Harrison cites "the use of f(x) to represent both application of a function f to an argument x, and the image under f of a subset, x, of f's domain".

External Links

• Section 2.2: Criticism and reconstruction from "Formalized Mathematics", by John Harrison
• "Strong Symbols", by Henning Thielemann (PDF Slides) Section 5: Common abuse of notation

See also

• Mathematical notation