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An equivalence class is defined as a subset of the form {x in X:xRa}, where a is an element of X and the notation "xRy" is used to mean that there is an equivalence relation ...

An equivalence relation on a set X is a subset of X×X, i.e., a collection R of ordered pairs of elements of X, satisfying certain properties. Write "xRy" to mean (x,y) is an ...

Experimental mathematics is a type of mathematical investigation in which computation is used to investigate mathematical structures and identify their fundamental properties ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...

In mathematics, a formula is a fact, rule, or principle that is expressed in terms of mathematical symbols. Examples of formulas include equations, equalities, identities, ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

The mean triangle area of a triangle picked inside a regular hexagon with unit area is A^_=289/3888 (Woolhouse 1867, Pfiefer 1989). This is a special case of a general ...