Advanced book on Mathematics Olympiad

(ff) #1

792 Index of Notation


〈−→v,−→w〉 inner (dot) product of vectors−→v and−→w


−→v ·−→w dot product of vectors−→v and−→w


−→v ×−→w cross-product of vectors−→v and−→w


x greatest integer not exceedingx


{x} fractional part ofx, equal tox−x


∑n
i= 1 ai the suma^1 +a^2 +···+an


∏n
i= 1 ai the producta^1 ·a^2 ···an


n! nfactorial, equal ton(n− 1 )··· 1


x∈A elementxis in setA


A⊂BAis a subset ofB


A∪B the union of the setsAandB


A∩B the intersection of the setsAandB


A\B the set of the elements ofAthat are not inB


A×B the Cartesian product of the setsAandB


P(A) the family of all subsets of the setA


∅ the empty set


a≡b(modc) ais congruent tobmoduloc, i.e.,a−bis divisible byc


a|badividesb


gcd(a, b) greatest common divisor ofaandb


(n
k


)

binomial coefficientnchoosek
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