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A function f is said to have a upper bound C if f(x)<=C for all x in its domain. The least upper bound is called the supremum. A set is said to be bounded from above if it ...

The Darboux integral, also called a Darboux-Stieltjes integral, is a variant of the Stieltjes integral that is defined as a common value for the lower and upper Darboux ...

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

The supremum is the least upper bound of a set S, defined as a quantity M such that no member of the set exceeds M, but if epsilon is any positive quantity, however small, ...

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...

Let b(k) be the number of 1s in the binary expression of k, i.e., the binary digit count of 1, giving 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, ... (OEIS A000120) for k=1, 2, .... ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...