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Unformatted text preview:  f ( x )  ≥ C  g ( x )  whenever x > k. e.g.: Since 8 x 3 + 5 x 2 + 6 ≥ 8 x 3 for all x ≥ 0. Therefore, 8 x 3 + 5 x 2 + 6 = Ω( x 3 ). 1 7. BigΘ notation Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers. f ( x ) = Θ( g ( x )) if f ( x ) = O ( g ( x )) and f ( x ) = Ω( g ( x )) . It is read as “ f ( x ) is bigTheta of g ( x )”, or f ( x ) is of order g ( x ). e.g. 1 + 2 + ··· + n is of order n 2 , i.e., 1 + 2 + ··· + n = Θ( n 2 ) . 8. Theorem: Let f ( x ) = a n x n + a n1 x n1 + ··· + a 1 x + a , where a n , . . . , a are real numbers and a n n = 0. Then f ( x ) is of order x n , i.e. f ( x ) = Θ( x n ). 2...
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 Winter '08
 Staff
 Rational number

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