In matematica una sezione di Dedekind, che prende il nome da Richard Dedekind, in un insieme totalmente ordinato S è una partizione di esso, (A, B), tale che A è un taglio iniziale senza un massimo.La sezione stessa è concettualmente il "divario" tra A e B.I casi originali e più importanti sono le sezioni di Dedekind dei numeri razionali e i numeri reali.

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations.Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields.These properties, such as …

Brunswick (/ ˈ b ʁ œ n s w i k / ; en allemand standard Braunschweig / ˈ b ʁ a ʊ̯ n ʃ v a ɪ̯ k / Écouter ; en bas-allemand Brunswiek / ˈ b r ɔ ˑ n s v i ː k /) est une ville du Nord de l'Allemagne située dans le Land de Basse-Saxe.Avec une population de 249 405 habitants en 2019, Brunswick est la deuxième plus grande ville de Basse-Saxe, après Hanovre sa capitale. ...

In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve".This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers).. The term was introduced in 1956 in a paper by Gardiner, …

In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of whether …

The absolute complement of A is usually denoted by A c. Other notations include ¯, ′,,.. Examples. Assume that the universe is the set of integers.If A is the set of odd numbers, then the complement of A is the set of even numbers. If B is the set of multiples of 3, then the complement of B is the set of numbers congruent to 1 or 2 modulo 3 (or, in simpler terms, the integers that …

Thus Dedekind infinite sets contain subsets that correspond bijectively with the natural numbers. Dedekind finite naturally means that every injective self-map is also surjective. Kuratowski finiteness is defined as follows. Given any set S, the binary operation of union endows the powerset P(S) with the structure of a semilattice.

In mathematics, the cardinality of a set is a measure of the "number of elements" of the set.For example, the set = {,,} contains 3 elements, and therefore has a cardinality of 3. Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them.

The Principles of Mathematics (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical.. The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference. It reported on developments by Giuseppe Peano, Mario Pieri, …