theorem

the·o·rem

T0151400 (thē′ər-əm, thîr′əm)n.1. An idea that has been demonstrated as true or is assumed to be so demonstrable.2. Mathematics A proposition that has been or is to be proved on the basis of explicit assumptions.

[Late Latin theōrēma, from Greek, from theōrein, to look at, from theōros, spectator; see theory.]

theorem

(ˈθɪərəm) n (Logic) maths logic a statement or formula that can be deduced from the axioms of a formal system by means of its rules of inference[C16: from Late Latin theōrēma, from Greek: something to be viewed, from theōrein to view] theorematic, theoremic, theorematical adj ˌtheoreˈmatically adv

the•o•rem

(ˈθi ər əm, ˈθɪər əm)

n. 1. Math. a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas. 2. a rule or law, esp. one expressed by an equation or formula. 3. Logic. a proposition that can be deduced from the premises or assumptions of a system. 4. an idea, method, or statement generally accepted as true or worthwhile without proof. [1545–55; < Late Latin theōrēma < Greek theṓrēma spectacle, object of contemplation, theorem =theōrē-, variant s. of theōreîn to observe, derivative of theōrós person sent to consult an oracle, spectator + -ma resultative n. suffix] the`o•re•mat′ic (-əˈmæt ɪk) adj.

the·o·rem

(thē′ər-əm, thîr′əm) A mathematical statement whose truth can be proved on the basis of a given set of axioms or assumptions.

Thesaurus

Noun	1.	theorem - a proposition deducible from basic postulatesbinomial theorem - a theorem giving the expansion of a binomial raised to a given powerproposition - (logic) a statement that affirms or denies something and is either true or false
	2.	theorem - an idea accepted as a demonstrable truthidea, thought - the content of cognition; the main thing you are thinking about; "it was not a good idea"; "the thought never entered my mind"Bayes' theorem - (statistics) a theorem describing how the conditional probability of a set of possible causes for a given observed event can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each cause

theorem

noun proposition, statement, formula, rule, principle, thesis, hypothesis, deduction, dictum He postulated a theorem and proved it.

theorem

nounA broad and basic rule or truth:axiom, fundamental, law, principle, universal.

Translations

定理法则

theorem

(ˈθiərəm) nounespecially in mathematics, something that has been or must be proved to be true by careful reasoning. a geometrical theorem. （数）定理，法则

theorem

theorem,

in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiomaxiom,
in mathematics and logic, general statement accepted without proof as the basis for logically deducing other statements (theorems). Examples of axioms used widely in mathematics are those related to equality (e.g.
..... Click the link for more information. in that a proofproof,
in mathematics, finite sequence of propositions each of which is either an axiom or follows from preceding propositions by one of the rules of logical inference (see symbolic logic).
..... Click the link for more information. 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 deFermat, Pierre de
, 1601–65, French mathematician. A magistrate whose avocation was mathematics, Fermat is known as a founder of modern number theory and probability theory.
..... Click the link for more information. ); 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.

Theorem

a statement, in some deductive theory, that has been or is to be proved (seeDEDUCTION). Examples of deductive theories are provided by mathematics, logic, theoretical mechanics, and some branches of physics. Every such theory consists of theorems that are proved one after another on the basis of previously proved theorems. The first statements in the deductive process are accepted without proof and thus form the logical basis of the given area of the theory. Such primitive statements are called axioms.

In the formulation of a theorem, a distinction is made between the hypothesis and the conclusion. Consider, for example, the following two theorems: (1) If the sum of the digits in a number is divisible by 3, then the number is itself divisible by 3. (2) If one of the angles in a triangle is a right angle, then the other two angles are acute. In these examples the word “if” is followed by the hypothesis of the theorem, and the word “then” is followed by the conclusion. Every theorem can be expressed in this form. For example, the theorem “Any angle inscribed in a semicircle is a right angle” can be expressed “If an angle is inscribed in a semicircle, then the angle is a right angle.”

The converse of a theorem expressed in the form “If..., then...” is obtained by interchanging the hypothesis and the conclusion. A theorem and its converse are converses of each other. In general, the validity of a theorem does not imply the validity of its converse. For example, the converse of theorem (1) is true, but the converse of theorem (2) is false. If a theorem and its converse are both true, then the hypothesis of either theorem is a necessary and sufficient condition for the validity of the conclusion (seeNECESSARY AND SUFFICIENT CONDITIONS).

If the hypothesis and conclusion of a theorem are replaced by their negations, then the inverse of the given theorem is obtained. The inverse of a theorem is equivalent to the theorem’s converse. Moreover, the converse of the inverse of a theorem is equivalent to the original theorem. Consequently, the validity of a theorem can be demonstrated by both a direct and an indirect proof. An indirect proof, also known as reductio ad absurdum, involves showing that the negation of the hypothesis of the theorem follows from the negation of the theorem’s conclusion. This method of proof is very widely used in mathematics.

theorem

[′thir·əm] (mathematics) A proven mathematical statement.

theorem

Maths Logic a statement or formula that can be deduced from the axioms of a formal system by means of its rules of inference

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Synonyms for theorem

noun proposition

Synonyms

Synonyms for theorem

noun a broad and basic rule or truth

Synonyms

Words related to theorem

noun a proposition deducible from basic postulates

Related Words

noun an idea accepted as a demonstrable truth

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