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Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...

Two totally ordered sets (A,<=) and (B,<=) are order isomorphic iff there is a bijection f from A to B such that for all a_1,a_2 in A, a_1<=a_2 iff f(a_1)<=f(a_2) (Ciesielski ...

An oriented link is a link for which each connected component has been given an orientation. As oriented links are equivalent, if there is an orientation preserving ...

A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

Given a statistical distribution with measured mean, statistical median, mode, and standard deviation sigma, Pearson's first skewness coefficient, also known as the Pearson ...

Pickover's sequence gives the starting positions in the decimal expansion of pi (ignoring the leading 3) in which the first n digits of e occur (counting the leading 2). So, ...

The partial differential equation (1+u_y^2)u_(xx)-2u_xu_yu_(xy)+(1+u_x^2)u_(yy)=0 (correcting a typo in Zwillinger 1997, p. 134).

A group theoretic operation which is useful in the study of complex atomic spectra. A plethysm takes a set of functions of a given symmetry type {mu} and forms from them ...

The theorem in set theory and logic that for all sets A and B, B=(A intersection B^_) union (B intersection A^_)<=>A=emptyset, (1) where A^_ denotes complement set of A and ...

Any ideal of a ring which is strictly smaller than the whole ring. For example, 2Z is a proper ideal of the ring of integers Z, since 1 not in 2Z. The ideal <X> of the ...