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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 . Well 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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This note was uploaded on 08/31/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at University of California, Berkeley.
 Summer '08
 STRAIN
 Math

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