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Pressing the On button (green) is an idempotent operation, since it has the same effect whether done once or multiple times. Likewise, pressing Off is idempotent. Idempotence ( UK : / ˌ ɪ d ɛ m ˈ p oʊ t ən s / , [ 1 ] US : / ˈ aɪ d ə m -/ ) [ 2 ] is the property of certain operations in mathematics and computer science whereby they can ...
setx is idempotent because the second application of setx to 3 has the same effect on the system state as the first application: x was already set to 3 after the first application, and it is still set to 3 after the second application. A pure function is idempotent if it is idempotent in the mathematical sense. For instance, consider the ...
In computer science, a deterministic algorithm is an algorithm that, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states.
The summation of idempotent endomorphisms corresponds to the decomposition of the unity of R: =, which is necessarily a finite sum; in particular, must be a finite set. For example, take R = M n ( D ) {\displaystyle R=\operatorname {M} _{n}(D)} , the ring of n -by- n matrices over a division ring D .
An idempotent a + I in the quotient ring R / I is said to lift modulo I if there is an idempotent b in R such that b + I = a + I. An idempotent a of R is called a full idempotent if RaR = R. A separability idempotent; see Separable algebra. Any non-trivial idempotent a is a zero divisor (because ab = 0 with neither a nor b being zero, where b ...
An element e in a ring R is a full idempotent when e 2 = e and ReR = R. P {\displaystyle {\mathcal {P}}} is Morita invariant if and only if whenever a ring R satisfies P {\displaystyle {\mathcal {P}}} , then so does eRe for every full idempotent e and so does every matrix ring M n R for every positive integer n ;
An idempotent e: A → A is said to split if there is an object B and morphisms f: A → B, g : B → A such that e = g f and 1 B = f g. The Karoubi envelope of C , sometimes written Split(C) , is the category whose objects are pairs of the form ( A , e ) where A is an object of C and e : A → A {\displaystyle e:A\rightarrow A} is an ...
In mathematics, an idempotent binary relation is a binary relation R on a set X (a subset of Cartesian product X × X) for which the composition of relations R ∘ R is the same as R. [ 1 ] [ 2 ] This notion generalizes that of an idempotent function to relations.