 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.[154555; < 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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IIn 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 steppingstones 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 theoremFermat's last theoremGödel's theoremRolle's theoremmean value theorems* * *
▪ logic and mathematicsin 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 socalled 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.* * *
Universalium. 2010.