the positive integers
11Proof that the sum of the reciprocals of the primes diverges — In the third century BC, Euclid proved the existence of infinitely many prime numbers. In the 18th century, Leonhard Euler proved a stronger statement: the sum of the reciprocals of all prime numbers diverges. Here, we present a number of proofs… …
12Characterizations of the exponential function — In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent …
13Arithmetic complexity of the discrete Fourier transform — See Fast Fourier transform#Bounds on complexity and operation counts for a general summary of this issue.Bounds on the multiplicative complexity of FFTIn his PhD thesis in 1987 [1] , Michael Heidman focus on the arithmetic theory of complexity… …
14Denotational semantics of the Actor model — The denotational semantics of the Actor model is the subject of denotational domain theory for Actors. The historical development of this subject is recounted in [Hewitt 2008b]. Contents 1 Actor fixed point semantics 2 Compositionality in… …
15Criticism of the APL programming language — The APL programming language has been used since the mid 1960s on mainframe computers and has itself evolved in step with computers and the computing market. APL is not widely used, but minimalistic and high level by design, at several points in… …
16Logic and the philosophy of mathematics in the nineteenth century — John Stillwell INTRODUCTION In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the… …
17Algorithm characterizations — The word algorithm does not have a generally accepted definition. Researchers are actively working in formalizing this term. This article will present some of the characterizations of the notion of algorithm in more detail. This article is a… …
18set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …
19Basel problem — The Basel problem is a famous problem in number theory, first posed by Pietro Mengoli in 1644, and solved by Leonhard Euler in 1735. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler s solution brought… …
20Partially ordered set — The Hasse diagram of the set of all subsets of a three element set {x, y, z}, ordered by inclusion. In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering,… …
