Grundvallarkenningum

Grundvallarkenningum is the Icelandic term for fundamental theorems, a class of results in mathematics that establish essential relationships and serve as cornerstones of their theories. The specific theorems designated as grundvallarkenningar vary by field, but all share the role of identifying core principles that enable further results and applications.

Examples commonly regarded as grundvallarkenningar include: The fundamental theorem of arithmetic states that every integer greater than 1 can be factored uniquely into primes, up to the order of the factors. The fundamental theorem of algebra states that every non-constant polynomial with complex coefficients has a complex root; equivalently, the complex numbers form an algebraically closed field. The fundamental theorem of calculus links differentiation and integration; Part 1 shows that the derivative of an integral is the integrand for continuous functions, and Part 2 shows that the definite integral equals the net change of an antiderivative. The rank-nullity theorem states that for a linear map between finite-dimensional vector spaces, the dimension of the domain equals the sum of the dimensions of its kernel and image. The fundamental theorem of Galois theory establishes a correspondence between subgroups of the Galois group of a field extension and intermediate fields; this relationship explains why some polynomials are solvable by radicals.

In Icelandic mathematical discourse, grundvallarkenningum is used as a general label for central results, with the specific theorems included depending on context and historical usage.