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the idempotent endomorphisms of a vector space are its projections. If the set has elements, we can partition it into chosen fixed points and non-fixed points under , and then is the number of different idempotent functions. Hence, taking into account all possible partitions, = is the total number of possible idempotent functions on the set.
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.
As an example, VBA code written in Microsoft Access can establish references to the Excel, Word and Outlook libraries; this allows creating an application that – for instance – runs a query in Access, exports the results to Excel and analyzes them, and then formats the output as tables in a Word document or sends them as an Outlook email.
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 ...
The functions are simple data validation and data type checking functions. The data validation functions determine whether it is possible to convert or coerce the data value given as an argument to the function to the type implied by the function name, and return a Boolean value recording whether it was possible or not.
In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. [ 1 ] [ 2 ] That is, the matrix A {\displaystyle A} is idempotent if and only if A 2 = A {\displaystyle A^{2}=A} .
Idempotency of entailment is a property of logical systems that states that one may derive the same consequences from many instances of a hypothesis as from just one. This property can be captured by a structural rule called contraction, and in such systems one may say that entailment is idempotent if and only if contraction is an admissible rule.
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