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For any set theoretic formula f(x,t_1,t_2,...,t_n), In other words, for any formula and set A there is a subset of A consisting exactly of those elements which satisfy the ...

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...

Reverse Polish notation (RPN) is a method for representing expressions in which the operator symbol is placed after the arguments being operated on. Polish notation, in which ...

Let ||f|| be the supremum of |f(x)|, a real-valued function f defined on (0,infty). If f is twice differentiable and both f and f^('') are bounded, Landau (1913) showed that ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...

A root-finding algorithm also known as the tangent hyperbolas method or Halley's rational formula. As in Halley's irrational formula, take the second-order Taylor series ...

The Lagrange interpolating polynomial is the polynomial P(x) of degree <=(n-1) that passes through the n points (x_1,y_1=f(x_1)), (x_2,y_2=f(x_2)), ..., (x_n,y_n=f(x_n)), and ...

The cut elimination theorem, also called the "Hauptsatz" (Gentzen 1969), states that every sequent calculus derivation can be transformed into another derivation with the ...