the positive integers
1History of the Church-Turing thesis — This article is an extension of the history of the Church Turing thesis.The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …
2History of the Church–Turing thesis — This article is an extension of the history of the Church–Turing thesis. The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …
3Divergence of the sum of the reciprocals of the primes — The sum of the reciprocals of all prime numbers diverges, that is: This was proved by Leonhard Euler in 1737, and strengthens Euclid s 3rd century BC result that there are infinitely many prime numbers. There is a variety of proofs of Euler s… …
4Particular values of the Gamma function — The Gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer and half integer arguments, but no simple expressions are known for the values at rational points in… …
5Positive definite kernel — In operator theory, a positive definite kernel is a generalization of a positive matrix. Definition Let :{ H n } {n in {mathbb Z be a sequence of (complex) Hilbert spaces and :mathcal{L}(H i, H j)be the bounded operators from Hi to Hj . A map A… …
6Positive definite function on a group — In operator theory, a positive definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups. It can be viewed as a particular type of positive definite kernel where the underlying set has… …
7positive — adj. & n. adj. 1 formally or explicitly stated; definite, unquestionable (positive proof). 2 (of a person) convinced, confident, or overconfident in his or her opinion (positive that I was not there). 3 a absolute; not relative. b Gram. (of an… …
8The Decline of the West — Cover of Volume II, first edition, 1922 The Decline of the West (German: Der Untergang des Abendlandes), or The Downfall of the Occident, is a two volume work by Oswald Spengler, the first volume of which was published in the summer of 1918.… …
9The Infinite Assassin — L Assassin infini L Assassin infini Auteur Greg Egan Genre Nouvelle Pays d origine  Australie Éditeur Revue Interzone Collection Axiomatique …
10Construction of the real numbers — In mathematics, there are several ways of defining the real number system as an ordered field. The synthetic approach gives a list of axioms for the real numbers as a complete ordered field. Under the usual axioms of set theory, one can show that …
