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A module having dual properties with respect to a free module, as enumerated below. 1. Every free module is projective; every cofree module is injective. 2. For every module ...

A product of ANDs, denoted ^ _(k=1)^nA_k. The conjunctions of a Boolean algebra A of subsets of cardinality p are the 2^p functions A_lambda= union _(i in lambda)A_i, where ...

A notation for polyhedra which begins by specifying a "seed" polyhedron using a capital letter. The Platonic solids are denoted T (tetrahedron), O (octahedron), C (cube), I ...

A set is denumerable iff it is equipollent to the finite ordinal numbers. (Moore 1982, p. 6; Rubin 1967, p. 107; Suppes 1972, pp. 151-152). However, Ciesielski (1997, p. 64) ...

The total angular defect is the sum of the angular defects over all polyhedron vertices of a polyhedron, where the angular defect delta at a given polyhedron vertex is the ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

The first singular value k_1 of the elliptic integral of the first kind K(k), corresponding to K^'(k_1)=K(k_1), (1) is given by k_1 = 1/(sqrt(2)) (2) k_1^' = 1/(sqrt(2)). (3) ...

The set containing no elements, commonly denoted emptyset or emptyset, the former of which is used in this work. These correspond to Wolfram Language and TeX characters ...

The intersection Fl of the Gergonne line and the Soddy line. In the above figure, D^', E^', and F^' are the Nobbs points, I is the incenter, Ge is the Gergonne point, and S ...

Let a hotel have a denumerable set of rooms numbered 1, 2, 3, .... Then any finite number n of guests can be accommodated without evicting the current guests by moving the ...