This bold attempt is entirely factitious and verbal, and it is only his employment of various terms not generally used in such a connection ( axiom, theorem, corollary, etc.

A corollary of Artin's theorem is that alternative algebras are power-associative, that is, the subalgebra generated by a single element is associative.

A corollary to Kleene's recursion theorem states that for every Gödel numbering of the computable functions and every computable function, there is an index such that returns.

By the corollary to the recursion theorem, there is an index such that returns.

A consequence of the Jacobson density theorem is Wedderburn's theorem ; namely that any right artinian simple ring is isomorphic to a full matrix ring of n by n matrices over a division ring for some n. This can also be established as a corollary of the Artin – Wedderburn theorem.

* A corollary is a proposition that follows with little or no proof from one other theorem or definition.

No closed tours exist for smaller square boards besides the trivial case ( this is a corollary of the following theorem ).

2 ) The theorem is a quick corollary of the Alexander subbase theorem.

This follows from the following corollary of the theorem ( Cutland 1980: p. 202 ).

In mathematics a corollary typically follows a theorem.

The use of the term corollary, rather than proposition or theorem, is intrinsically subjective.

The importance of the corollary is often considered secondary to that of the initial theorem ; B is unlikely to be termed a corollary if its mathematical consequences are as significant as those of A.

* Freudenthal suspension theorem, a corollary of excision for homotopy groups.

If f is a non-constant entire function, then its image is dense in C. This might seem to be a much stronger result than Liouville's theorem, but it is actually an easy corollary.

Another immediate corollary of the theorem is that if a language defines an infinite set of equivalence classes, it is not regular.

It is a corollary of Gödel's incompleteness theorem that there is no deductive system ( that is, no notion of provability ) for second-order formulas that simultaneously satisfies these three desired attributes:

As a direct corollary, the Artin – Wedderburn theorem implies that every simple ring that is finite-dimensional over a division ring ( a simple algebra ) is a matrix ring.

* The result above is a corollary of a general theorem by Christiaan Huygens which is also known as gambler's ruin.

Strictly speaking, this is not a corollary of the theorem but rather a by-product of the proof.

The impact of noncompliance under the Wagner-Peyser Act is clear: the withdrawal of some $11 million a year of administrative funds which finance our employment service program or, as a corollary, the taking over by the Federal Government of its operation.

he further reasoned that frequent formulas in epic verse indicate oral composition, and assumed the slightly less likely corollary that oral epic is inclined towards the use of formulas.

Kant is not generally considered to be a modern anthropologist, however, as he never left his region of Germany nor did he study any cultures besides his own, and in fact, describes the need for anthropology as a corollary field to his own primary field of philosophy.

Finagle's Law of Dynamic Negatives ( also known as Finagle's corollary to Murphy's Law ) is usually rendered:

This is opposed to the idea of freedom as the capacity to " begin anew ," which Arendt sees as a corollary to the innate human condition of natality, or our nature as " new beginnings and hence beginners.

There is a widely recognized corollary that any such ulterior-motive invocation of Godwin's law will be unsuccessful.

The historical definition differs from the length-based standard in that a minute of arc, and hence a nautical mile, is not a constant length at the surface of the Earth but gradually lengthens in the north-south direction with increasing distance from the equator, as a corollary of the Earth's oblateness, hence the need for " mean " in the last sentence of the previous paragraph.

Egoism is a corollary of setting man's life as the moral standard.

A corollary to Rand's endorsement of self-interest is her rejection of the ethical doctrine of altruism — which she defined in the sense of Auguste Comte's altruism ( he coined the term ), as a moral obligation to live for the sake of others.

The corollary is that high-Z materials make good gamma-ray shields, which is the principal reason that lead ( Z

The pope sat briefly on two " pierced chairs " at the Lateran: "... the vulgar tell the insane fable that he is touched to verify that he is indeed a man " a sign that this corollary of the Pope Joan legend was still current in the Roman street.

* As an easy corollary of the Nikolov-Segal result above, any surjective discrete group homomorphism φ: G → H between profinite groups G and H is continuous as long as G is topologically finitely-generated.

* The first corollary is that employees who are dedicated to their current jobs should not be promoted for their efforts ( as in The Dilbert Principle ), and instead should be rewarded with, say, a pay raise, while remaining in their current position.

* The second corollary is that employees might be promoted only after being sufficiently trained to the new position.

As a corollary, every finite p-group is nilpotent.

*** The corollary from the previous two properties and De Morgan ’ s law is that is also closed under countable intersections: if A < sub > i </ sub >∈ for i = 1, 2 ,…, then also (∩< sub > i </ sub > A < sub > i </ sub >)∈

As a corollary, we obtain another proof of the infinitude of the prime numbers: for each F < sub > n </ sub >, choose a prime factor p < sub > n </ sub >; then the sequence

:* As a corollary, if the index of H in G is 2, or for a finite group the lowest prime p that divides the order of G, then H is normal, as the index of its core must also be p, and thus H equals its core, i. e., is normal.

The correlation of the corollary discharge signal with the actual afferent signal returned from the periphery can then be used to determine if, in fact, the intended action occurred as expected.

The most typical way of constructing new examples is the following corollary from the O ' Neill curvature formulas: if is a Riemannian manifold admitting a free isometric action of a Lie group G, and M has positive sectional curvature on all 2-planes orthogonal to the orbits of G, then the manifold with the quotient metric has positive sectional curvature.

The Hamiltonian case then becomes a corollary.

A related corollary is that if almost all prime ideals of K split completely in L, then in fact L

A corollary is that if the entries of an n by n matrix N are bounded by B, so | N < sub > ij </ sub >|≤ B for all i and j, then

The corollary Korean identifying title derives from Gihae in the Chinese sexagenary cycle of the calendar system then in use in Joseon.

As a corollary, if M and N are two manifolds, each with volume forms, then for any points, there are open neighborhoods U of m and V of n and a map such that the volume form on N restricted to the neighborhood V pulls back to volume form on M restricted to the neighborhood U:.

Add to this the corollary: there are secrets, then there are secrets.

A corollary then points out how it is possible in this way to determine the centripetal force for any given shape of orbit and center.

Indeed, the bounded convergence theorem ( a corollary of the dominated convergence theorem ) of real analysis states that if a sequence of functions on a set of finite measure is uniformly bounded and converges pointwise, then passage of the limit under the integral is valid.