theorem


theorem
theorematic /thee'euhr euh mat"ik, thear'euh-/, adj.theorematically, adv.
/thee"euhr euhm, thear"euhm/, 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, belief, method, or statement generally accepted as true or worthwhile without proof.
[1545-55; < LL theorema < Gk theórema spectacle, hence, subject for contemplation, thesis (to be proved), equiv. to theore-, var. s. of theoreîn to view + -ma n. suffix]

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I
In mathematics or logic, a statement whose validity has been established or proved.

It consists of a hypothesis and a conclusion, beginning with certain assumptions that are necessary and sufficient to establish a result. A system of theorems that build on and augment each other constitutes a theory. Within any theory, however, only statements that are essential, important, or of special interest are called theorems. Less important statements, usually stepping-stones in proofs of more important results, are called lemmas. A statement proved as a direct consequence of a theorem is a corollary of the theorem. Some theorems (and even lemmas and corollaries) are singled out and given titles (e.g., Gödel's theorem, fundamental theorem of algebra, fundamental theorem of calculus, Pythagorean theorem).
II
(as used in expressions)
Bernoulli's theorem
Fermat's last theorem
Gödel's theorem
Rolle's theorem
mean value theorems

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▪ logic and mathematics
      in mathematics and logic, a proposition or statement that is demonstrated. In geometry, a proposition is commonly considered as a problem (a construction to be effected) or a theorem (a statement to be proved). The statement “If two lines intersect, each pair of vertical angles is equal,” for example, is a theorem. The so-called fundamental theorem of algebra asserts that every (complex) polynomial equation in one variable has at least one complex root or solution. The Greeks also recognized a proposition lying between a theorem and a problem, the porism, directed to producing or finding what is proposed.

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Universalium. 2010.

Synonyms:
(to be demonstrated), , ,


Look at other dictionaries:

  • 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. [1913 Webster]… …   The Collaborative International Dictionary of English

  • Theorem — The o*rem, v. t. To formulate into a theorem. [1913 Webster] …   The Collaborative International Dictionary of English

  • Theorēm — (griech.), soviel wie Lehrsatz …   Meyers Großes Konversations-Lexikon

  • Theorem — Theorēm (grch.), Lehrsatz …   Kleines Konversations-Lexikon

  • Theorem — Theorem, griech. (das Wort mit allen damit verwandten Ausdrücken hat seine Wurzel in einem griech. Zeitworte, welches bedeutet: anschauen, besonders: innerlich, geistig anschauen, in seinen letzten Gründen etwas schauen), der Lehrsatz; t. atisch …   Herders Conversations-Lexikon

  • theorem — index inference, postulate, prescription (directive), principle (axiom), supposition Burton s Legal Thesaurus. William …   Law dictionary

  • Theorem — Theorem,das:⇨Lehrsatz …   Das Wörterbuch der Synonyme

  • theorem — (n.) 1550s, from M.Fr. théorème, from L.L. theorema, from Gk. theorema spectacle, speculation, in Euclid proposition to be proved, from theorein to consider (see THEORY (Cf. theory)) …   Etymology dictionary

  • theorem — *principle, axiom, fundamental, law …   New Dictionary of Synonyms

  • theorem — [n] explanation based on hypothesis and experiments assumption, axiom, belief, deduction, dictum, doctrine, formula, fundamental, law, postulate, principium, principle, proposition, rule, statement, theory, thesis; concepts 529,688,689 Ant. fact …   New thesaurus

  • theorem — ► NOUN 1) Physics & Mathematics a general proposition not self evident but proved by a chain of reasoning. 2) Mathematics a rule expressed by symbols or formulae. ORIGIN Greek the r ma speculation, proposition …   English terms dictionary


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