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Informally, the term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve A that is asymptotic to given ...

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any set a and a formula A(y) of a set x consisting of all elements of a satisfying A(y), exists x ...

Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...

Eisenstein's irreducibility criterion is a sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring Q[x]. The polynomial ...

Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in the Wolfram ...

A Hermitian form on a vector space V over the complex field C is a function f:V×V->C such that for all u,v,w in V and all a,b in R, 1. f(au+bv,w)=af(u,w)+bf(v,w). 2. ...

A sentential formula that contains at least one free variable (Carnap 1958, p. 24). A sentential variable containing no free variables (i.e., all variables are bound) is ...

A graph G that becomes disconnected when removing a suitable complete subgraph K, called a vertex cut, is said to be quasiseparable. The two simplest cases are those where K ...

The silver ratio is the quantity defined by the continued fraction delta_S = [2,2,2,...] (1) = 2+1/(2+1/(2+1/(2+...))) (2) (Wall 1948, p. 24). It follows that ...

Ergodic theory can be described as the statistical and qualitative behavior of measurable group and semigroup actions on measure spaces. The group is most commonly N, R, R-+, ...