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A set R of linear extensions of a partially ordered set P=(X,<=) is a realizer of P (and is said to realize P) provided that for all x,y in X, x<=y iff x is below y in every ...

"The reals" is a common way of referring to the set of real numbers and is commonly denoted R.

A pair of consecutive primes whose digits are rearrangements of each other, first considered by A. Edwards in Aug. 2001. The first few are (1913, 1931), (18379, 18397), ...

Each row and each column in the group multiplication table lists each of the group elements once and only once. From this, it follows that no two elements may be in the ...

The reciprocal differences are closely related to the divided difference. The first few are explicitly given by rho(x_0,x_1)=(x_0-x_1)/(f_0-f_1) (1) ...

The sum of reciprocal multifactorials can be given in closed form by the beautiful formula m(n) = sum_(n=0)^(infty)1/(n!...!_()_(k)) (1) = ...

Given a rectangle BCDE, draw EF=DE on an extension of BE. Bisect BF and call the midpoint G. Now draw a semicircle centered at G, and construct the extension of ED which ...

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

A mathematical relationship expressing f_n as some combination of f_i with i<n. When formulated as an equation to be solved, recurrence relations are known as recurrence ...

A quadrature (numerical integration) algorithm which has a number of desirable properties.