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An initial point that provides safe convergence of Newton's method (Smale 1981; Petković et al. 1997, p. 1).

The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

A vaguely defined branch of mathematics dealing with varieties, the Mordell conjecture, Arakelov theory, and elliptic curves.

Arrow's paradox, also called Arrow's impossibility theorem or the general possibility theorem, states that perfect democratic voting is impossible, not just in practice but ...

Let p be an odd prime, a be a positive number such that pa (i.e., p does not divide a), and let x be one of the numbers 1, 2, 3, ..., p-1. Then there is a unique x^', called ...

A pair of numbers m and n such that sigma(m)=sigma(n)=m+n-1, where sigma(m) is the divisor function. Beck and Najar (1977) found 11 augmented amicable pairs.

A subset B of a vector space E is said to be balanced if lambdaB subset= B whenever lambda is a scalar satisfying |lambda|<=1. Here, the notation lambdaB denotes the set ...

The Banach density of a set A of integers is defined as lim_(d->infty)max_(n)(|{A intersection [n+1,...,n+d]}|)/d, if the limit exists. If the lim is replaced with lim sup or ...

If a and b are integers not both equal to 0, then there exist integers u and v such that GCD(a,b)=au+bv, where GCD(a,b) is the greatest common divisor of a and b.

Given a set of objects S, a binary relation is a subset of the Cartesian product S tensor S.