Search Results for ""

Let S be the set of all possibilities that satisfy hypothesis H, and let S^' be the set of all possibilities that satisfy hypothesis H^'. Then H^' is a nested hypothesis ...

There are a number of attractive polyhedron compounds consisting of 30 octahedra. This compound will be implemented in a future version of the Wolfram Language as ...

A map is called "one-to-one" (or "1:1") if it is injective. However, being in "one-to-one correspondence" is synonymous with being a bijection. Unfortunately, this confusing ...

An n-dimensional open disk of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Krantz (1999, p. 3) uses the symbol D(x,r) ...

A paracompact space is a T2-space such that every open cover has a locally finite open refinement. Paracompactness is a very common property that topological spaces satisfy. ...

A perfect cubic polynomial can be factored into a linear and a quadratic term, x^3+y^3 = (x+y)(x^2-xy+y^2) (1) x^3-y^3 = (x-y)(x^2+xy+y^2). (2)

The point group C_1 is a group on a single element that is isomorphic to the trivial group. Its character table is given below. C_1 1 1 1

Polyrects are polyforms obtained from a rectangular grid, illustrated above. The numbers of polyrects with n=1, 2, ... components are 1, 2, 3, 9, 21, 68, 208, ... (OEIS ...

The volume of a prismatoid is equal to the sum of the volumes of a pyramid, a wedge, and a parallelepiped.

A topology on a set X whose open sets are the unions of open balls B(X_0,r)={x in x|g(x_0,x)<r}, where g is a pseudometric on X, x_0 is any point of X, and r>0. There is a ...