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Every real number is negative, 0, or positive. The law is sometimes stated as "For arbitrary real numbers a and b, exactly one of the relations a<b, a=b, a>b holds" (Apostol ...

The series sum_(j=1)^(infty)f_j(z) is said to be uniformly Cauchy on compact sets if, for each compact K subset= U and each epsilon>0, there exists an N>0 such that for all ...

A point lattice which can be constructed from an arbitrary parallelogram of unit area. For any such planar lattice, the minimum distance c between any two points is a ...

For a graph G and a subset S of the vertex set V(G), denote by N_G[S] the set of vertices in G which are in S or adjacent to a vertex in S. If N_G[S]=V(G), then S is said to ...

Lagrange's identity is the algebraic identity (sum_(k=1)^na_kb_k)^2=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2)-sum_(1<=k<j<=n)(a_kb_j-a_jb_k)^2 (1) (Mitrinović 1970, p. 41; Marsden ...

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of ordered individuals ...

As first shown by Meyer and Ritchie (1967), do-loops (which have a fixed iteration limit) are a special case of while-loops. A function that can be implemented using only ...

A set T of integers is said to be recursively enumerable if it constitutes the range of a recursive function, i.e., if there exists a recursive function that can eventually ...

Bowling, known as "ten pins" throughout most of the world, is a game played by rolling a heavy ball down a long narrow track and attempting to knock down ten pins arranged in ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...