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elementary theorem

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  • Elementary proof — In mathematics a proof is said to be elementary if it avoids difficult ideas from distant areas of mathematics. For example, the term is used in number theory to refer to proofs that make no use of complex analysis. An elementary proof in… …   Wikipedia

  • Elementary class — In the branch of mathematical logic called model theory, an elementary class (or axiomatizable class) is a class consisting of all structures satisfying a fixed first order theory. Contents 1 Definition 2 Conflicting and alternative terminology …   Wikipedia

  • Elementary symmetric polynomial — In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial P can be expressed as a polynomial in elementary… …   Wikipedia

  • Elementary function — This article discusses the concept of elementary functions in differential algebra. For simple functions see the list of mathematical functions. For the concept of elementary form of an atom see oxidation state. In mathematics, an elementary… …   Wikipedia

  • Theorem — The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements …   Wikipedia

  • Elementary group theory — In mathematics, a group is defined as a set G and a binary operation on G , called product and denoted by infix * . Product obeys the following rules (also called axioms). Let a , b , and c be arbitrary elements of G . Then: *A1, Closure. a * b… …   Wikipedia

  • Elementary particle — In particle physics, an elementary particle or fundamental particle is a not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic …   Wikipedia

  • Elementary divisors — In algebra, the elementary divisors of a module over a principal ideal domain occur in one form of the structure theorem for finitely generated modules over a principal ideal domain.If R is a PID and M a finitely generated R module, then M is… …   Wikipedia

  • Prime number theorem — PNT redirects here. For other uses, see PNT (disambiguation). In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are… …   Wikipedia

  • Löwenheim–Skolem theorem — In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The… …   Wikipedia

  • Pythagorean theorem — See also: Pythagorean trigonometric identity The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c) …   Wikipedia

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