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Longman Dictionary of Contemporary English
▪ To help prove this theorem we shall need to call upon the following result, which is known as the Division Algorithm.
▪ I could prove theorem after theorem in linear algebra.
▪ That is, S is empty, and this proves the theorem.
▪ He pretended to show how an uneducated slave boy could be led to prove Pythagoras' theorem for doubling the square.
▪ Although Mr Quine has no important theorem to his name he wrote on mathematical logic with ingenuity and wit.
▪ Application of the Hopf bifurcation theorem shows that a periodic solution appears at the wi 1 bifurcation { 79 }.
▪ Consequently we can use the quotient theorem to prove that is a tensor.
▪ Examples of the use of this theorem are given in 2.2.3.
▪ The non-substitution theorem then applies, and prices are again determined independently of demand conditions.
▪ This theorem was first established by Sylvester.
▪ You might even stumble upon a theorem or two in your researches.
The Collaborative International Dictionary

Theorem \The"o*rem\, n. [L. theorema, Gr. ? a sight, speculation, theory, theorem, fr. ? to look at, ? a spectator: cf. F. th['e]or[`e]me. See Theory.]

  1. That which is considered and established as a principle; hence, sometimes, a rule.

    Not theories, but theorems (?), the intelligible products of contemplation, intellectual objects in the mind, and of and for the mind exclusively.

    By the theorems, Which your polite and terser gallants practice, I re-refine the court, and civilize Their barbarous natures.

  2. (Math.) A statement of a principle to be demonstrated.

    Note: A theorem is something to be proved, and is thus distinguished from a problem, which is something to be solved. In analysis, the term is sometimes applied to a rule, especially a rule or statement of relations expressed in a formula or by symbols; as, the binomial theorem; Taylor's theorem. See the Note under Proposition, n., 5.

    Binomial theorem. (Math.) See under Binomial.

    Negative theorem, a theorem which expresses the impossibility of any assertion.

    Particular theorem (Math.), a theorem which extends only to a particular quantity.

    Theorem of Pappus. (Math.) See Centrobaric method, under Centrobaric.

    Universal theorem (Math.), a theorem which extends to any quantity without restriction.


Theorem \The"o*rem\, v. t. To formulate into a theorem.

Douglas Harper's Etymology Dictionary

1550s, from Middle French théorème (16c.) and directly from Late Latin theorema, from Greek theorema "spectacle, sight," in Euclid "proposition to be proved," literally "that which is looked at," from theorein "to look at, behold" (see theory).


n. 1 (context mathematics English) A mathematical statement of some importance that has been proven to be true. Minor theorems are often called ''propositions''. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called ''lemmas'' 2 (context mathematics colloquial nonstandard English) A mathematical statement that is expected to be true; as, http://en.wikipedi

  1. org/wiki/Fermat's%20Last%20Theorem (as which it was known long before it was proved in the 1990s.) 3 (context logic English) a syntactically correct expression that is deducible from the given axioms of a deductive system v

  2. (context transitive English) to formulate into a theorem

  1. n. a proposition deducible from basic postulates

  2. an idea accepted as a demonstrable truth


In mathematics, a theorem is a statement that has been proved on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, which is experimental.

Many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called hypotheses or premises. In light of the interpretation of proof as justification of truth, the conclusion is often viewed as a necessary consequence of the hypotheses, namely, that the conclusion is true in case the hypotheses are true, without any further assumptions. However, the conditional could be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol.

Although they can be written in a completely symbolic form, for example, within the propositional calculus, theorems are often expressed in a natural language such as English. The same is true of proofs, which are often expressed as logically organized and clearly worded informal arguments, intended to convince readers of the truth of the statement of the theorem beyond any doubt, and from which a formal symbolic proof can in principle be constructed. Such arguments are typically easier to check than purely symbolic ones—indeed, many mathematicians would express a preference for a proof that not only demonstrates the validity of a theorem, but also explains in some way why it is obviously true. In some cases, a picture alone may be sufficient to prove a theorem. Because theorems lie at the core of mathematics, they are also central to its aesthetics. Theorems are often described as being "trivial", or "difficult", or "deep", or even "beautiful". These subjective judgments vary not only from person to person, but also with time: for example, as a proof is simplified or better understood, a theorem that was once difficult may become trivial. On the other hand, a deep theorem may be simply stated, but its proof may involve surprising and subtle connections between disparate areas of mathematics. Fermat's Last Theorem is a particularly well-known example of such a theorem.

Usage examples of "theorem".

So in the theorem of the Parallelogram of Velocities we have a strictly geometrical theorem, whose content is in the narrowest sense kinematic.

Kepler-Newton case on the very lines of our treatment of the two parallelogram theorems.

In this assertion we encounter a misconception exactly like the one in the statement that the theorem of the parallelogram of forces follows by logical necessity from the theorem of the parallelogram of velocities.

The Tycho and Dov Danladi, Soli too-they struggled all their lives to prove the Great Theorem.

The same sort of computer program that plays checkers can also be made to solve theorems on inequalities such as that pictured here, where one is asked to prove that the angle ACE is less than ABE.

Any such argument claims to provide a counterexample to their general theorem, and if one such counterexample is true the general theorem must be false.

The edicts of the Mull therefore rest not so much upon exigencies of the moment as upon fundamental theorems.

Our device will verify some of the most important theorems of our, and your, mathematics, simply by a direct inspection of cases, all the way to infinity.

In dock areas I found the packing houses, seeking to investigate perspectives pure as theorems, the self-mastery of these concrete structures, invulnerable to melancholy.

And yet, Holmes went on to explain, this same man was immune to suspicion, a respected mathematics professor in fact, and the celebrated author of a brilliant treatise on the binomial theorem as well as of The Dynamics of an Asteroid, a book of rarefied scientific scholarship much ahead of its time.

He kept the name as a convenience and, under it, published two treatises, on the binomial theorem and small planetary bodies, which drew on future knowledge.

I want him to yadder childishly to me about the binomial theorem after breakfast.

Nothing that the mind of man can conceive is perfect, save it be a mathematical theorem.

All I did was take advantage of a cautionary theorem in Advanced Symbolic Logic: The apparency of an answer can be mistaken for the answer.

He was the first to prove geometric theorems of the sort codified by Euclid three centuries later - for example, the proposition that the angles at the base of an isosceles triangle are equal.