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Let S be a nonempty set of real numbers that has a lower bound. A number c is the called the greatest lower bound (or the infimum, denoted infS) for S iff it satisfies the ...

For any positive integer k, there exists a prime arithmetic progression of length k. The proof is an extension of Szemerédi's theorem.

Gregory's formula is a formula that allows a definite integral of a function to be expressed by its sum and differences, or its sum by its integral and difference (Jordan ...

Grelling's paradox, also known as the Grelling-Nelson paradox or heterological paradox, is a semantic paradox that arises by defining "heterological" to mean "a word which ...

A grid usually refers to two or more infinite sets of evenly-spaced parallel lines at particular angles to each other in a plane, or the intersections of such lines. The two ...

The Griewank function is a function widely used to test the convergence of optimization functions. The Griewank function of order n is defined by ...

Sequences of integers generated in the Collatz problem. For example, for a starting number of 7, the sequence is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...

A root-finding algorithm which makes use of a third-order Taylor series f(x)=f(x_n)+f^'(x_n)(x-x_n)+1/2f^('')(x_n)(x-x_n)^2+.... (1) A root of f(x) satisfies f(x)=0, so 0 ...

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 ...

Let F(m,n) be the number of m×n (0,1)-matrices with no adjacent 1s (in either columns or rows). For n=1, 2, ..., F(n,n) is given by 2, 7, 63, 1234, ... (OEIS A006506). The ...