Unformatted text preview: • (1 , 1) ∈ S • If ( a,b ) ∈ S , then (2 a, 3 b ) ∈ S Prove that if ( a,b ) ∈ S , then ( a,b ) = (2 n , 3 n ) for some nonnegative integer n . We’ll go by structural induction: • BC: (1 , 1) = (2 , 3 ) • IH: Suppose ( a,b ) ∈ S and ( a,b ) = (2 k , 3 k ). • IS: Then (2 a, 3 b ) = (2 · 2 k , 3 · 3 k ) = (2 k +1 , 3 k +1 ) Thus, by structural induction it works for all ( a,b ) ∈ S...
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 Summer '08
 STRAIN
 Math, Logic, Mathematical Induction, Recursion, Structural induction, Rob Bayer

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