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An expression in mathematics which does not have meaning and so which is not assigned an interpretation. For example, division by zero is undefined in the field of real ...

A horizontal line placed above multiple quantities to indicate that they form a unit. It is most commonly used to denote 1. A radical (sqrt(12345)), 2. Repeating decimals ...

A diagonal slash resembling the solidus, but with slightly less slant, used to denote division for in-line equations such as a/b, 1/(x-1)^2, etc.

Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

A theorem of fundamental importance in spectroscopy and angular momentum theory which provides both (1) an explicit form for the dependence of all matrix elements of ...

If there is an integer 0<x<p such that x^2=q (mod p), (1) i.e., the congruence (1) has a solution, then q is said to be a quadratic residue (mod p). Note that the trivial ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...