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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 This definition is obsolete, but is often used in schoolbooks.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

sin−1, cos−1, tan−1

but they are no multiplicative inverses. It does prevent the use of all sorts of difficult names for these functions.


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