Fundamental Theorem

The fundamental theorem of a field of mathematics is the theorem considered central to that field. The naming of such a theorem is not necessarily based on how often it is used or the difficulty of its proofs.

For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus, which are two distinct branches that were not obviously related.

The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory.

The mathematical literature sometimes refers to the fundamental lemma of a field. The term lemma is conventionally used to denote a proven proposition which is used as a stepping stone to a larger result rather than as a useful statement in-and-of itself. The fundamental lemma of a field is often, but not always, the same as the fundamental theorem of that field.

Other articles related to "theorem, fundamental theorem, theorems, fundamental theorems, fundamental":

List Of Theorems - F
... Riesz theorem (measure theory) FWL theorem (economics) Faltings' theorem (diophantine geometry) Farrell–Markushevich theorem (complex analysis) Fáry's ...
Proof Of Impossibility - The Fundamental Theorem of Arithmetic
... Gödel used these theorems in his proof (see below, more in Nagel and Newman p ... First theorem (cf Hardy and Wright, p ... Second theorem fundamental theorem of arithmetic (cf Hardy and Wright p ...
Signed Graph - Fundamental Theorem
... This is the first theorem of signed graphs (Harary, 1953) ... It generalizes the theorem that an ordinary (unsigned) graph is bipartite if and only if every cycle has even length ... To prove Harary's theorem, one shows by induction that Σ can be switched to be all positive if and only if it is balanced ...
Non-mathematical Fundamental Theorems
... There are also a number of "fundamental theorems" not directly related to mathematics Fundamental theorem of arbitrage-free pricing Fisher's fundamental theorem of natural selection Fundamental theorems of ...
Integral - Introduction
... actual calculation of integrals, the fundamental theorem of calculus, due to Newton and Leibniz, is the fundamental link between the operations of differentiating and integrating ... operator d, known as the exterior derivative is introduced, and the fundamental theorem becomes the more general Stokes' theorem, from which Green's theorem, the ...

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