triangle axiom

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• Axiom — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… …   Wikipedia

• Triangle inequality — In mathematics, the triangle inequality states that for any triangle, the length of a given side must be less than or equal to the sum of the other two sides but greater than or equal to the difference between the two sides.In Euclidean geometry… …   Wikipedia

• Least upper bound axiom — The least upper bound axiom, also abbreviated as the LUB axiom, is an axiom of real analysis stating that if a nonempty subset of the real numbers has an upper bound, then it has a least upper bound. It is an axiom in the sense that it cannot be… …   Wikipedia

• Pasch's axiom — In geometry, Pasch s axiom, is a result of plane geometry used by Euclid, but yet which cannot be derived from Euclid s postulates. Its axiomatic role was discovered by Moritz Pasch.The axiom states that, in the plane, :A line which intersects… …   Wikipedia

• Tarski's axioms — Tarski s axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry, called elementary, that is formulable in first order logic with identity, and requiring no set theory. Other modern axiomizations of… …   Wikipedia

• Triangulated category — A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t category is a triangulated category with a t… …   Wikipedia

• Logic 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… …   History of philosophy

• mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

• History of geometry — Geometry (Greek γεωμετρία ; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre modern mathematics, the other being the study of numbers. Classic geometry… …   Wikipedia

• Parallel postulate — In geometry, the parallel postulate, also called Euclid s fifth postulate since it is the fifth postulate in Euclid s Elements , is a distinctive axiom in what is now called Euclidean geometry. It states that: If a line segment intersects two… …   Wikipedia

• Scientology beliefs and practices — Scientology is, according to its own texts, the study and handling of the spirit in relationship to itself, others and all of life. [cite web | url=http://www.scientology.org/en US/religion/presentation/pg006.html | title=Introduction to… …   Wikipedia