Peano system

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• Peano axioms — In mathematical logic, the Peano axioms, also known as the Dedekind Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used… …   Wikipedia

• Peano-Axiom — ℕ Die natürlichen Zahlen sind die beim Zählen verwendeten Zahlen 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 usw. Oft wird auch die 0 (Null) zu den natürlichen Zahlen gerechnet. Sie bilden bezüglich der Addition und der Multiplikation einen (additiv und… …   Deutsch Wikipedia

• Peano-Arithmetik — Die Peano Arithmetik (erster Stufe) ist eine Theorie der Arithmetik, also der Natürlichen Zahlen, innerhalb der Prädikatenlogik erster Stufe. Als Axiome werden die Peano Axiome verwendet, wobei das Induktionsaxiom durch ein Axiomenschema ersetzt… …   Deutsch Wikipedia

• Axiomatic system — In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems. An axiomatic… …   Wikipedia

• Number system — This article is about different sets of numbers. For different methods of expressing numbers with symbols, see numeral system. In mathematics, a number system is a set of numbers, (in the broadest sense of the word), together with one or more… …   Wikipedia

• Axiomatisches System — Dieser Artikel oder Abschnitt bedarf einer Überarbeitung. Näheres ist auf der Diskussionsseite angegeben. Hilf mit, ihn zu verbessern, und entferne anschließend diese Markierung. Ein Axiomensystem (auch: Axiomatisches System) ist im engeren Sinn… …   Deutsch Wikipedia

• L-system — An L system or Lindenmayer system is a parallel rewriting system, namely a variant of a formal grammar (a set of rules and symbols), most famously used to model the growth processes of plant development, but also able to model the morphology of a …   Wikipedia

• Deductive system — A deductive system (also called a deductive apparatus of a formal system) consists of the axioms (or axiom schemata) and rules of inference that can be used to derive the theorems of the system.[1] Such a deductive system is intended to preserve… …   Wikipedia

• formal system — In logic, a formal language together with a deductive apparatus by which some well formed formulas can be derived from others. Each formal system has a formal language composed of primitive symbols that figure in certain rules of formation… …   Universalium

• logic, history of — Introduction       the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic       There was a medieval tradition according to which the Greek philosopher …   Universalium

• Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… …   Wikipedia