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The identity substitution, which maps every variable to itself, is the neutral element of substitution composition. A substitution σ is called idempotent if σσ = σ, and hence tσσ = tσ for every term t. When x i ≠t i for all i, the substitution { x 1 ↦ t 1, …, x k ↦ t k} is idempotent if and only if none of the variables x i ...
In propositional logic, disjunction elimination [1] [2] (sometimes named proof by cases, case analysis, or or elimination) is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.
In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation , and can loosely be thought of as using the chain rule "backwards."
To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1.
In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations.
Process of elimination is a logical method to identify an entity of interest among several ones by excluding all other entities. In educational testing , it is a process of deleting options whereby the possibility of an option being correct is close to zero or significantly lower compared to other options.
The cut-elimination theorem (or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in part I of his landmark 1935 paper "Investigations in Logical Deduction" [ 1 ] for the systems LJ and LK formalising intuitionistic and classical logic respectively.
In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2] [3] [4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.