Definitions
from The Century Dictionary.
 noun In multiple algebra, a quantity which multiplied into itself gives itself. Ordinary unity is idempotent.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics (
computing ) Describing an action which, when performed multiple times, has no further effect on its subject after the first time it is performed.  adjective mathematics Said of an element of an
algebraic structure (such as agroup orsemigroup ) with abinary operation : that when the element operates on itself, the result is equal to itself.  adjective mathematics Said of a
binary operation : that all of the distinct elements it can operate on are idempotent (in the sense given just above).  noun An idempotent
ring or other structure
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adjective unchanged in value following multiplication by itself
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
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Examples

On your last few paragraphs, I'm not sure I get your comment about it being "idempotent" with creationist second law arguments  though I can't say I'm terribly familiar with those.
Rabett Run EliRabett 2009

My first instinct would be to stop using the pretentious word "idempotent"

My first instinct would be to stop using the pretentious word "idempotent", which is a symptom of the Haskellers 'disease of assuming that math terminology is a good way to concisely communicate concepts to nonmathematicians ...

He was interested in the structure of rings of linear operators and realized that the central idempotents, that is, the operators E that commuted with all other operators in the ring under multiplication (that is, EL = LE for all L in the ring) and which were idempotent under multiplication
The Algebra of Logic Tradition Burris, Stanley 2009

As mentioned earlier, Boole gave inadequate sets of equational axioms for his system, originally starting with the two laws due to Gregory plus his idempotent law; these were accompanied by De Morgan's inference rule that one could carry out the same operation
The Algebra of Logic Tradition Burris, Stanley 2009

The act of providing information is idempotent, at least from the perspective of the user; any sideeffects of a CARBON request are the responsibility of the entity that handles them, just like with an HTTP GET request.

A together with • and Â·, along with 0 and 1, forms a ring with identity in which every element is idempotent.
The Mathematics of Boolean Algebra Monk, J. Donald 2009

For example, as long as the arguments satisfy the relevant condition Î¾, Ã— is idempotent, commutative, and associative, and it interacts with + in conformity with the the following distribution laws:

These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent.
The Mathematics of Boolean Algebra Monk, J. Donald 2009

His fascination with the possibilities of ordinary algebra led him to consider questions such as: What would logic be like if the idempotent law were replaced by the law X3 = X?
The Algebra of Logic Tradition Burris, Stanley 2009
john commented on the word idempotent
"An idempotent operation in math is one that has the same effect whether you apply it once, or more than once. Multiplying a number by zero is idempotent: 4 x 0 x 0 x 0 is the same as 4 x 0."
 "RESTful Web Services," pg. 102.
August 24, 2007
ruzuzu commented on the word idempotent
From the Wikipedia page for Benjamin Peirce: "In algebra, he was notable for the study of associative algebras. He first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the Peirce decomposition." (https://en.wikipedia.org/w/index.php?title=Benjamin_Peirce&oldid=1079065220)
August 9, 2022