arithmetic of order types

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• Order type — In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection f: X → Y such that both f and its inverse are monotone (order… …   Wikipedia

• Arithmetic — tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word ἀριθμός, arithmos “number”) is the oldest and most elementary branch of mathematics, used b …   Wikipedia

• Arithmetic logic unit — schematic symbol Cascadable 8 …   Wikipedia

• Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… …   Wikipedia

• Order theory — For a topical guide to this subject, see Outline of order theory. Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as… …   Wikipedia

• Ordinal arithmetic — In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an… …   Wikipedia

• List of first-order theories — In mathematical logic, a first order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties. PreliminariesFor every natural mathematical structure… …   Wikipedia

• Fixed-point arithmetic — In computing, a fixed point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point ( e.g. , after the decimal point . in English decimal notation). Fixed point… …   Wikipedia

• First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …   Wikipedia

• Arbitrary-precision arithmetic — In computer science, arbitrary precision arithmetic indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed precision… …   Wikipedia

• Greek arithmetic, geometry and harmonics: Thales to Plato — Ian Mueller INTRODUCTION: PROCLUS’ HISTORY OF GEOMETRY In a famous passage in Book VII of the Republic starting at Socrates proposes to inquire about the studies (mathēmata) needed to train the young people who will become leaders of the ideal… …   History of philosophy