The concept and theory of Kolmogorov Complexity is based on a crucial theorem first discovered by Ray Solomonoff, who published it in 1960, describing it in " A Preliminary Report on a General Theory of Inductive Inference " as part of his invention of algorithmic probability.

His concept " Dyson's transform " led to one of the most important lemmas of Olivier Ramaré's theorem that every even integer can be written as a sum of no more than six primes.

Also, it makes the concept of " provability " and thus of " theorem ", a clear concept that only depends on the chosen system of axioms of the theory, and not on the choice of a proof system.

A fundamental concept of Lorentz's theory in 1895 was the " theorem of corresponding states " for terms of order v / c.

: For the theorem of propositional logic based on the same concept, see double negation.

Gödel's incompleteness theorem shows that no consistent, recursively enumerable theory ( that is, one whose theorems form a recursively enumerable set ) in which the concept of natural numbers can be expressed, can include all true statements about them.

The notion of a theorem is deeply intertwined with the concept of proof.

The concept of a formal theorem is fundamentally syntactic, in contrast to the notion of a " true proposition " in which semantics are introduced.

The book introduces the concept of spherical triangle ( figures formed of three great circle arcs, which he named " trilaterals ") and proves Menelaus ' theorem on collinearity of points on the edges of a triangle ( which may have been previously known ) and its analog for spherical triangles.

The concept is important to formulate the Baire category theorem.

He also claims to have proven a derivation of Bayes ' theorem from the concept of fuzzy subsethood.

In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals ( or some other equivalent formulation of completeness ), which is not an algebraic concept.

Bell ’ s theorem states that the concept of local realism, favoured by Einstein, yields predictions that disagree with those of quantum mechanical theory.

Central to the theory was the concept of uniform continuity and the theorem stating that every continuous function on a closed interval is uniformly continuous.

This theorem introduced the concept of comparing the ratio between the input distortion and the output distortion of an audio amplifier.

Arguments for the mean speed theorem ( above ) require the modern mathematical concept of limit, so Bradwardine had to use arguments of his day.

The concept of normality is important because normal matrices are precisely those to which the spectral theorem applies: a matrix A is normal if and only if it can be represented by a diagonal matrix Λ and a unitary matrix U by the formula

The concept of dual cell structure, which Henri Poincaré used in his proof of his Poincaré duality theorem, contained the germ of the idea of cohomology, but this was not seen until later.

Amongst his most original contributions were: his " Conjecture II " ( still open ) on Galois cohomology ; his use of group actions on Trees ( with H. Bass ); the Borel-Serre compactification ; results on the number of points of curves over finite fields ; Galois representations in ℓ-adic cohomology and the proof that these representations have often a " large " image ; the concept of p-adic modular form ; and the Serre conjecture ( now a theorem ) on mod-p representations that made Fermat's last theorem a connected part of mainstream arithmetic geometry.

* Transversality theorem, a concept related to the intersection of manifolds in topology

An application of the channel capacity concept to an additive white Gaussian noise ( AWGN ) channel with B Hz bandwidth and signal-to-noise ratio S / N is the Shannon – Hartley theorem:

Merton's concept of the self-fulfilling prophecy stems from the Thomas theorem, which states that " If men define situations as real, they are real in their consequences.

A concept of responsibility is in process of articulation and establishment.

National responsibility for individual welfare is a concept not limited to the United States or even to the Western nations.

Recognizing that the Rule of Law is `` a dynamic concept which should be employed not only to safeguard the civil and political rights of the individual in a free society '', the Congress asserted that it also included the responsibility `` to establish social, economic, educational and cultural conditions under which his legitimate aspirations and dignity may be realized ''.

Whether a concept analogous to the principle of internal responsibility operates in a nation's external relations is less obvious and more difficult to establish.

) The concept of nationalism is the political principle that epitomizes and glorifies the territorial state as the characteristic type of socal structure.

Historically, however, the concept is one that has been of marked benefit to the people of the Western civilizational group.

But it is more than irony: one of the main reasons why nationalism is no longer a tenable concept is because it has spread throughout the planet.

It is interesting, however, that despite this strong upsurge in Southern writing, almost none of the writers has forsaken the firmly entrenched concept of the white-suited big-daddy colonel sipping a mint julep as he silently recounts the revenue from the season's cotton and tobacco crops ; ;

A broader concept of imitation is needed, one which acknowledges that true invention is important, that the artist's creativity in part transcends the non-artistic causal factors out of which it arises.

Who will deny that in a vast portion of the South the Federal action is incompatible with the Jeffersonian concept of `` the consent of the governed ''??

For it is their catastrophic concept of the Anglo-Saxon invasions rather than Kemble's gradualist approach which dominates the field.

But beginning, for all practical purposes, with Frederick Seebohm's English Village Community scholars have had to reckon with a theory involving institutional and agrarian continuity between Roman and Anglo-Saxon times which is completely at odds with the reigning concept of the Anglo-Saxon invasions.

It is ironic that Washington is having to struggle so for a concept that for six years it bypassed as unreasonable.

The concept of labor as a special class is outmoded, and in the task confronting America as bastion of the free world, labor must learn to put the national interest first if it is itself to survive.

The most fundamental concept of the new approach to economic aid is the focusing of our attention, our resources, and our energies on the effort to promote the economic and social development of the less developed countries.

While it is easy enough to ridicule Hawkins' pronouncement in Pleas Of The Crown from a metaphysical point of view, the concept of the `` oneness '' of a married couple may reflect an abiding belief that the communion between husband and wife is such that their actions are not always to be regarded by the criminal law as if there were no marriage.

That we had the wit and wisdom to adopt Mr. Lowell's concept and make it the base for our processes of selection is one reason why our selections have been, it may be said truly, pretty uniformly good.

It is this sort of experience that makes the concept of high fidelity of real musical significance for the home music listener.

The concept of trans-illumination ( as shown by the photo on p. 92 ), as just one example, offers an entirely new approach to lighting problems -- no matter what industry is involved.