# idempotent

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## idempotent

[¦i‚dem¦pōt·ənt] (mathematics)

An element

*x*of an algebraic system satisfying the equation*x*^{2}=*x*.An algebraic system in which every element

*x*satisfies*x*^{2}=*x*.## idempotent

(1)A function f : D -> D is idempotent if

f (f x) = f x for all x in D.

I.e. repeated applications have the same effect as one. This can be extended to functions of more than one argument, e.g. Boolean & has x & x = x. Any value in the image of an idempotent function is a fixed point of the function.

f (f x) = f x for all x in D.

I.e. repeated applications have the same effect as one. This can be extended to functions of more than one argument, e.g. Boolean & has x & x = x. Any value in the image of an idempotent function is a fixed point of the function.

## idempotent

(2)This term can be used to describe C header files, which
contain common definitions and declarations to be included by
several source files. If a header file is ever included twice
during the same compilation (perhaps due to nested #include
files), compilation errors can result unless the header file
has protected itself against multiple inclusion; a header file
so protected is said to be idempotent.

## idempotent

(3)The term can also be used to describe an initialisation
subroutine that is arranged to perform some critical action
exactly once, even if the routine is called several times.

## idempotent

An operation that produces the same results no matter how many times it is performed. For example, a database query that does not change any data in the database is idempotent.Functions can be designed as idempotent if all that is desired is to ensure a certain operation has been completed. For example, with an idempotent delete function, if a request to delete a file is successfully completed for one program, all subsequent requests to delete that file from other programs would return the same success confirmation message. In a non-idempotent delete function, an error would be returned for the second and subsequent requests indicating that the file was not there.

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