different between nullipotent vs idempotent

English

Etymology

Latin roots, nullus (“not any”) +? potent (“having power”) – literally, “having no power”.

Adjective

nullipotent (not comparable)

1. (mathematics, computing) Describing an action which has no side effect. Queries are typically nullipotent: they return useful data, but do not change the data structure queried. Contrast with idempotent.
2. (biology) Incapable of developing into any cell type; compare pluripotent

Usage notes

In computing, contrast with idempotent: both refer to the potential result of performing an action on an object multiple times, the difference being that an idempotent action's result would be the same as performing it one time, while the nullipotent action's result would be the same as performing it zero times.

In other words, a nullipotent action has no side effects – performing it multiple times is the same as performing it zero times. An idempotent action has no further side effects after the first time performing it – performing it multiple times is the same as performing it one time.

Coordinate terms

• (computing): idempotent
• (biology): pluripotent

Related terms

• fixed point
• idempotent
• impotent
• nilpotent
• nullipotence
• omnipotent
• pluripotent
• potent
• unipotent
• ventripotent
• no-op

English

Etymology

Latin roots, idem (“same”) +? potent (“having power”) – literally, “having the same power”.

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

Pronunciation

• (US) IPA^(key): /a?.d?m?po?.t?nt/, /?.d?m?po?.t?nt/

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: such 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

Noun

idempotent (plural idempotents)

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

References

• “idempotent” at FOLDOC

German

Pronunciation

Adjective

idempotent

1. idempotent

Swedish

Adjective

idempotent

1. idempotent

Turkish

Adjective

idempotent

1. idempotent