idempotent

English

Etymology

(deprecated template usage) [etyl] Latin roots, idem (“same”) +‎ potent (“having power”) – literally, “having the same power”.

Coined 1870 by American mathematician Benjamin Peirce in context of algebra.

Pronunciation

• IPA^(key): /aɪ.dəmˈpoʊ.tənt/, /ɪ.dəmˈpoʊ.tənt/

Adjective

idempotent (not comparable)

1. (mathematics, computing) Said of a function: describing an action which, when performed multiple times on the same subject, has no further effect on its subject after the first time it is performed.

   A projection operator is idempotent.

2. (mathematics) Said of an element of an algebraic structure with a binary operation (such as a group or semigroup): when the element operates on itself, the result is equal to itself.

   Every finite semigroup has an idempotent element.

   Every group has a unique idempotent element: namely, its identity element.

3. (mathematics) 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.

4. (mathematics) Said of an algebraic structure: having an idempotent operation (in the sense above).

Usage notes

See the Usage notes section of nullipotent.

Coordinate terms

• nilpotent
• nullipotent

Related terms

• idempotence
• nilpotent
• nullipotent
• unipotent

Translations

mathematics: an action which, when performed multiple time, has no further effect on its subject after the first time it is performed

• Chinese:

  Mandarin: 冪等／幂等 (mìděng)

• Czech: idempotentní (cs)
• Danish: idempotent
• Esperanto: idempotento
• Finnish: idempotentti (fi)
• German: idempotent (de)
• (deprecated template usage) {{trans-mid}}
• Icelandic: sjálfvalda
• Japanese: 冪等 (べきとう, bekitō)
• Polish: idempotentny
• Russian: идемпоте́нтный (ru) (idempoténtnyj)
• Swedish: idempotent (sv)
• Turkish: idempotent

mathematics: Said of an element of an algebraic structure with a binary operation: that when the element operates on itself, the result is equal to itself

• Chinese:

  Mandarin: 冪等／幂等 (mìděng)

• Esperanto: idempotento
• (deprecated template usage) {{trans-mid}}
• Finnish: idempotentti (fi)
• Greek: ταυτοδύναμος m (taftodýnamos)
• Spanish: idempotente

Said of a binary operation: that all of the distinct elements it can operate on are idempotent

• Finnish: idempotentti (fi)
• (deprecated template usage) {{trans-mid}}

Noun

idempotent (plural idempotents)

1. (mathematics) An idempotent element.
2. (mathematics) An idempotent structure.

References

• “idempotent” at FOLDOC

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German

Pronunciation

• Audio:

  (file)

Adjective

idempotent

1. idempotent

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Swedish

Adjective

idempotent

1. idempotent

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Turkish

Adjective

idempotent

1. idempotent