corollary


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theorem

theorem, in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiom in that a proof is required for its acceptance. A lemma is a theorem that is demonstrated as an intermediate step in the proof of another, more basic theorem. A corollary is a theorem that follows as a direct consequence of another theorem or an axiom. There are many famous theorems in mathematics, often known by the name of their discoverer, e.g., the Pythagorean Theorem, concerning right triangles. One of the most famous problems of number theory was the proof of Fermat's Last Theorem (see Fermat, Pierre de); the theorem states that for an integer n greater than 2 the equation xn+yn=zn admits no solutions where x, y, and z are also integers.
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corollary

Logic a proposition that follows directly from the proof of another proposition
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
By Theorem 42, together with Theorem 8 or Corollary 10, we have the following.
Scott speculated that the internal copy of our voice produced by corollary discharge can be generated even when there isn't any external sound, meaning that the sound we hear when we talk inside our heads is actually the internal prediction of the sound of our own voice.
For [alpha] = 1, [lambda] = 1/2 in above corollary, we find below the result justifying the well-known result Marx [4] and Strohhacker [9] that K [subset] [S.sup.*](1/2).
Corollary 3 If A is open subset of X, then [T.sub.[zeta]] [|.sub.A] [subset not equal to] [(T [|.sub.A]).sub.[zeta]].
Thus Corollary 3.1 coincides with Proposition 1 in [4].
It is known that all commutative locally m-pseudoconvex (in particular, commutative locally m-convex) algebras are simplicial (see [5], Corollary 5; for the case of complete algebras see [4], Proposition 2, and [11], Corollary 7.1.14; and for the case of locally m-convex algebras see [42], p.
Corollary 3.1 Consider labeled decomposable combinatorial structures whose component generating function is of alg-log type with an algebraic exponent 0 < [alpha] < 1.
Finally, we point out that the Nikiforov and Uvarov technique is required in order to obtain the new Corollary 3.10.
Last year's drama Spanglish featured a Mexican maid as its central plot device, but only as a corollary to a crisis in an upper-middle-class marriage.
Lastly, corollary to the realization that more cushioning doesn't mean less injury lies a discussion of how an orthotic works.
Martinot places particular emphais on Albert Memmi's theory of racial construction as a "negative valuation of the other" along with its corollary: the positive self-valuation by the aggressive, privileged group.