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theorem

theorem, in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiom in that a proof 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 de); 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.

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theorem

the·o·rem / ˈ[unvoicedth]ēərəm; ˈ[unvoicedth]i(ə)r-/ • n. Physics & Math. a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths. ∎  a rule in algebra or other branches of mathematics expressed by symbols or formulae. DERIVATIVES: the·o·re·mat·ic / ˌ[unvoicedth]ēərəˈmatik; ˌ[unvoicedth]i(ə)rə-/ adj.

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theorem

theorem general proposition demonstrable by argument. XVI. — F. théorème or late L. theōrēma — Gr. theṓrēma speculation, theory, proposition to be proved, f. theōreîn look at, f. theōrós spectator (see THEORY).
So theoretic(al) †speculative, contemplative; pert to theory. XVII. — late L. theōrēticus — Gr. theōrētikós. Hence theoretician XIX.

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theorem

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