Binomial theorem

Binomial theorem
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]

Not theories, but theorems (?), the intelligible products of contemplation, intellectual objects in the mind, and of and for the mind exclusively. --Coleridge. [1913 Webster]

By the theorems, Which your polite and terser gallants practice, I re-refine the court, and civilize Their barbarous natures. --Massinger. [1913 Webster]

2. (Math.) A statement of a principle to be demonstrated. [1913 Webster]

Note: 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. [1913 Webster]

{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. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • Binomial theorem — Binomial Bi*no mi*al, a. 1. Consisting of two terms; pertaining to binomials; as, a binomial root. [1913 Webster] 2. (Nat. Hist.) Having two names; used of the system by which every animal and plant receives two names, the one indicating the… …   The Collaborative International Dictionary of English

  • binomial theorem — n. the general formula for the expansion of any binomial when raised to a power that is a positive whole number; the expansion of (a + b) n: discovered by Omar Khayyám and generalized by Sir Isaac Newton (Ex.: (a + b) 2 = a2 + 2ab + b2) …   English World dictionary

  • Binomial theorem — The binomial coefficients appear as the entries of Pascal s triangle. In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power… …   Wikipedia

  • binomial theorem — Math. the theorem giving the expansion of a binomial raised to any power. [1865 70] * * * In algebra, a formula for expansion of the binomial (x + y) raised to any positive integer power. A simple case is the expansion of (x + y)2, which is x2 +… …   Universalium

  • binomial theorem — noun a theorem giving the expansion of a binomial raised to a given power • Topics: ↑statistics • Hypernyms: ↑theorem • Part Holonyms: ↑probability theory, ↑theory of probability …   Useful english dictionary

  • binomial theorem — noun Date: 1753 a theorem that specifies the expansion of a binomial of the form (x + y)n as the sum of n + 1 terms of which the general term is of the form n!/((n k)! k!) x(n k) yk where k takes on values from 0 to n …   New Collegiate Dictionary

  • binomial theorem — bino′mial the′orem n. math. the theorem giving the expansion of a binomial raised to any power • Etymology: 1865–70 …   From formal English to slang

  • binomial theorem — noun A formula giving the expansion of a binomial such as raised to any positive integer power, i.e. . Its possible to expand the power into a sum of terms of the form where the coefficient of each term is a positive integer. For example …   Wiktionary

  • binomial theorem — n. mathematical formula that provides the expansion of a binomial raised to any power …   English contemporary dictionary

  • binomial theorem — noun a formula for finding any power of a binomial without multiplying at length …   English new terms dictionary

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