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- Idempotence abstract "Idempotence (/ˌaɪdɨmˈpoʊtəns/ EYE-dəm-POH-təns) is the property of certain operations in mathematics and computer science, that can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in which it is connected to the property of referential transparency).The term was introduced by Benjamin Peirce in the context of elements of algebras that remain invariant when raised to a positive integer power, and literally means "(the quality of having) the same power", from idem + potence (same + power).There are several meanings of idempotence, depending on what the concept is applied to:A unary operation (or function) is idempotent if, whenever it is applied twice to any value, it gives the same result as if it were applied once; i.e., ƒ(ƒ(x)) ≡ ƒ(x). For example, the absolute value function, where abs(abs(x)) ≡ abs(x).A binary operation is idempotent if, whenever it is applied to two equal values, it gives that value as the result. For example, the function giving the maximum value of two equal values is idempotent: max (x, x) ≡ x.Given a binary operation, an idempotent element (or simply an "idempotent") for the operation is a value for which the operation, when given that value for both of its operands, gives that value as the result. For example, the number 1 is an idempotent of multiplication: 1 × 1 = 1.↑".
- Idempotence wikiPageExternalLink HPL-BRIMS-96-24.pdf.
- Idempotence wikiPageExternalLink idempotent.
- Idempotence wikiPageExternalLink index.html.
- Idempotence wikiPageID "14972".
- Idempotence wikiPageLength "17001".
- Idempotence wikiPageOutDegree "95".
- Idempotence wikiPageRevisionID "675763490".
- Idempotence wikiPageWikiLink Absolute_value.
- Idempotence wikiPageWikiLink Abstract_algebra.
- Idempotence wikiPageWikiLink Basis_(linear_algebra).
- Idempotence wikiPageWikiLink Benjamin_Peirce.
- Idempotence wikiPageWikiLink Binary_operation.
- Idempotence wikiPageWikiLink Biordered_set.
- Idempotence wikiPageWikiLink Boolean_algebra.
- Idempotence wikiPageWikiLink Cambridge_University_Press.
- Idempotence wikiPageWikiLink Category:Abstract_algebra.
- Idempotence wikiPageWikiLink Category:Binary_operations.
- Idempotence wikiPageWikiLink Category:Closure_operators.
- Idempotence wikiPageWikiLink Category:Mathematical_relations.
- Idempotence wikiPageWikiLink Category:Theoretical_computer_science.
- Idempotence wikiPageWikiLink Closure_(topology).
- Idempotence wikiPageWikiLink Closure_operator.
- Idempotence wikiPageWikiLink Complex_number.
- Idempotence wikiPageWikiLink Computer_science.
- Idempotence wikiPageWikiLink Constant_function.
- Idempotence wikiPageWikiLink Cyclic_code.
- Idempotence wikiPageWikiLink Database.
- Idempotence wikiPageWikiLink Elevator.
- Idempotence wikiPageWikiLink Event_Stream_Processing.
- Idempotence wikiPageWikiLink Event_stream_processing.
- Idempotence wikiPageWikiLink FOLDOC.
- Idempotence wikiPageWikiLink Fixed_point_(mathematics).
- Idempotence wikiPageWikiLink Floor_and_ceiling_functions.
- Idempotence wikiPageWikiLink Floor_function.
- Idempotence wikiPageWikiLink Formal_grammar.
- Idempotence wikiPageWikiLink Free_On-line_Dictionary_of_Computing.
- Idempotence wikiPageWikiLink Function_(mathematics).
- Idempotence wikiPageWikiLink Function_composition.
- Idempotence wikiPageWikiLink Functional_programming.
- Idempotence wikiPageWikiLink Hazewinkel,_Michiel.
- Idempotence wikiPageWikiLink Hypertext_Transfer_Protocol.
- Idempotence wikiPageWikiLink Idempotent_matrix.
- Idempotence wikiPageWikiLink Idempotent_of_a_code.
- Idempotence wikiPageWikiLink Idempotent_relation.
- Idempotence wikiPageWikiLink Idempotent_semiring.
- Idempotence wikiPageWikiLink Identity_element.
- Idempotence wikiPageWikiLink Identity_function.
- Idempotence wikiPageWikiLink Indecomposable_module.
- Idempotence wikiPageWikiLink Integer_sequence.
- Idempotence wikiPageWikiLink Intersection_(set_theory).
- Idempotence wikiPageWikiLink Involution_(mathematics).
- Idempotence wikiPageWikiLink Iterated_function.
- Idempotence wikiPageWikiLink Join_(mathematics).
- Idempotence wikiPageWikiLink Join_and_meet.
- Idempotence wikiPageWikiLink Kleene_plus.
- Idempotence wikiPageWikiLink Kleene_star.
- Idempotence wikiPageWikiLink Lattice_(order).
- Idempotence wikiPageWikiLink Linear_algebra.
- Idempotence wikiPageWikiLink Linear_map.
- Idempotence wikiPageWikiLink Linear_transformation.
- Idempotence wikiPageWikiLink List_of_matrices.
- Idempotence wikiPageWikiLink Load-store_architecture.
- Idempotence wikiPageWikiLink store_architecture.
- Idempotence wikiPageWikiLink Logical_conjunction.
- Idempotence wikiPageWikiLink Logical_disjunction.
- Idempotence wikiPageWikiLink Mathematics.
- Idempotence wikiPageWikiLink Maxima_and_minima.
- Idempotence wikiPageWikiLink Maximum.
- Idempotence wikiPageWikiLink Meet_(mathematics).
- Idempotence wikiPageWikiLink Method_(computer_programming).
- Idempotence wikiPageWikiLink Method_(computer_science).
- Idempotence wikiPageWikiLink Michiel_Hazewinkel.
- Idempotence wikiPageWikiLink Modular_arithmetic.
- Idempotence wikiPageWikiLink Module_(algebra).
- Idempotence wikiPageWikiLink Module_(mathematics).
- Idempotence wikiPageWikiLink Modulo_arithmetic.
- Idempotence wikiPageWikiLink Motorola_68000.
- Idempotence wikiPageWikiLink Multiplication.
- Idempotence wikiPageWikiLink Nilpotent.
- Idempotence wikiPageWikiLink Operation_(mathematics).
- Idempotence wikiPageWikiLink Page_fault.
- Idempotence wikiPageWikiLink Plane_(geometry).
- Idempotence wikiPageWikiLink Plane_(mathematics).
- Idempotence wikiPageWikiLink Power_set.
- Idempotence wikiPageWikiLink Projection_(linear_algebra).
- Idempotence wikiPageWikiLink Projector_(linear_algebra).
- Idempotence wikiPageWikiLink Pure_function.
- Idempotence wikiPageWikiLink Real_number.
- Idempotence wikiPageWikiLink Referential_transparency_(computer_science).
- Idempotence wikiPageWikiLink Ring_(mathematics).
- Idempotence wikiPageWikiLink Semiring.
- Idempotence wikiPageWikiLink Side_effect_(computer_science).
- Idempotence wikiPageWikiLink Subroutine.
- Idempotence wikiPageWikiLink Topological_space.
- Idempotence wikiPageWikiLink Truth_value.
- Idempotence wikiPageWikiLink Unary_operation.
- Idempotence wikiPageWikiLink Union_(set_theory).
- Idempotence wikiPageWikiLink Vector_space.
- Idempotence wikiPageWikiLink Wikt:idem.