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The power tower of order k is defined as a^^k=a^(a^(·^(·^(·^a))))_()_(k), (1) where ^ is Knuth up-arrow notation (Knuth 1976), which in turn is defined by ...

If x takes only nonnegative values, then P(x>=a)<=(<x>)/a. (1) To prove the theorem, write <x> = int_0^inftyxP(x)dx (2) = int_0^axP(x)dx+int_a^inftyxP(x)dx. (3) Since P(x) is ...

The word configuration is sometimes used to describe a finite collection of points p=(p_1,...,p_n), p_i in R^d, where R^d is a Euclidean space. The term "configuration" also ...

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

The Farey sequence F_n for any positive integer n is the set of irreducible rational numbers a/b with 0<=a<=b<=n and (a,b)=1 arranged in increasing order. The first few are ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

A Cunningham number is a binomial number of the form C^+/-(b,n)=b^n+/-1 with b>1 and n positive integers. Bases b^k which are themselves powers need not be considered since ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...

Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...