Unformatted text preview: a P ( P (3stooges) ) has .............. many elements. b Let P ∞ denote the collection of all inﬁnite subsets of N . Deﬁne a relation ≈ on P ∞ by: A ≈ B IFF A ∩ B is inﬁnite. Stmt “ Relation ≈ is transitive ” is: T F c An explicit bijection F : N , ± Z is If n is even , then F ( n ) := .......................... . If n is odd , then F ( n ) := ........................... . d To the interval J := ( π 2 , π 2 ) , deﬁne a bijection g : ( , 1 ) , ± J by g ( x ) := ............................. . In terms of this g and a trigonometric function, deﬁne a bijection h : ( , 1 ) , ± R by h ( x ) := .................... . e The map f ( k,n ) := 2 k · [1 + 2 n ] is a bijection from N × N → Z + . And f 1 (112) = ( ....... , ....... ). End of ClassV V1: 65pts V2: 85pts V3: 95pts Total: 245pts...
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 Fall '09
 LARSON

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