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The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

A sorting algorithm which makes n passes over a set of n elements, in each pass selecting the smallest element and deleting it from the set. This algorithm has running time ...

A notation is a set of well-defined rules for representing quantities and operations with symbols.

A map which uses a set of rules to transform elements of a sequence into a new sequence using a set of rules which "translate" from the original sequence to its ...

The set of all zero-systems of a group G is denoted B(G) and is called the block monoid of G since it forms a commutative monoid under the operation of zero-system addition ...

For a subgroup H of a group G and an element x of G, define xH to be the set {xh:h in H} and Hx to be the set {hx:h in H}. A subset of G of the form xH for some x in G is ...

Let f be a function defined on a set A and taking values in a set B. Then f is said to be an injection (or injective map, or embedding) if, whenever f(x)=f(y), it must be the ...

A map defined by one or more polynomials. Given a field K, a polynomial map is a map f:K^n->K^m such that for all points (x_1,...,x_n) in K^n, ...