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Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product ...

A reducible fraction is a fraction p/q such that GCD(p,q)>1, i.e., p/q can be written in reduced form. A fraction that is not reducible is said to be irreducible. For ...

The versine, also known as the "versed sine," is a little-used trigonometric function defined by versin(z) = 2sin^2(1/2z) (1) = 1-cosz, (2) where sinz is the sine and cosz is ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

A function possessing a single period in the complex plane is said to be singly periodic, of often simply periodic. Singly periodic functions include the trigonometric ...

A bilinear form on a real vector space is a function b:V×V->R that satisfies the following axioms for any scalar alpha and any choice of vectors v,w,v_1,v_2,w_1, and w_2. 1. ...

Each Cartan matrix determines a unique semisimple complex Lie algebra via the Chevalley-Serre, sometimes called simply the "Serre relations." That is, if (A_(ij)) is a k×k ...

The cross-correlation of two complex functions f(t) and g(t) of a real variable t, denoted f*g is defined by f*g=f^_(-t)*g(t), (1) where * denotes convolution and f^_(t) is ...

A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

A complex line bundle is a vector bundle pi:E->M whose fibers pi^(-1)(m) are a copy of C. pi is a holomorphic line bundle if it is a holomorphic map between complex manifolds ...