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Mathematicians use these words as follows:
every logical statement is either true or false;
a theorem is a statement that has been proved true.

The"o*rem (?), n. [L. theorema, Gr. a sight, speculation, theory, theorem, fr. to look at, a spectator: cf. F. th'eoreme. 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. Coleridge.

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

2. Math.

A statement of a principle to be demonstrated.

⇒ 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.

The"o*rem, v. t.

To formulate into a theorem.

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