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Abuse of notation
An abuse of notation occurs when a mathematical notation is used in a way that is not formally correct.
Example 1
The imaginary unit is sometimes written as
whatever that may be. The square root of a negative number is however not defined. You never see
because i has no real value. This definition is obsolete, but is often used in schoolbooks.
Example 2
The inverse trigonometric functions are increasingly being written as
but they are no multiplicative inverses. It does prevent the use of all sorts of difficult names for these functions.