Definitions for idempotentˈaɪ dəmˈpoʊt nt, ˈɪd əm-
Random House Webster's College Dictionary
i•dem•po•tent*ˈaɪ dəmˈpoʊt nt, ˈɪd əm-
(adj.)(of a number or matrix) unchanged when multiplied by itself.
(n.)an idempotent element.
Origin of idempotent:
unchanged in value following multiplication by itself
"this matrix is idempotent"
An idempotent ring or other structure
Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed.
Said of an element of an algebraic structure (such as a group or semigroup) with a binary operation: that when the element operates on itself, the result is equal to itself.
Every group has a unique idempotent element: namely, its identity element.
Said of a binary operation: that all of the distinct elements it can operate on are idempotent (in the sense given just above).
Since the AND logical operator is commutative, associative, and idempotent, then it distributes with respect to itself. (This is useful for understanding one of the conjunction rules of simplification to Prenex Normal Form, if the universal quantifier is thought of as a "big AND".)
Origin: roots, – literally, “having the same power”.
The New Hacker's Dictionary
[from mathematical techspeak] Acting as if used only once, even if used multiple times. This term is often used with respect to 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. The term can also be used to describe an initialization subroutine that is arranged to perform some critical action exactly once, even if the routine is called several times.
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