Concept explainers
rcises 49-51 present incorrect proofs using mathematical induction. You rill need to identify an error in reasoningin each exercise.
51. What is wong with this ;;proof'?
'Theorem' For every positive integern, if1and y areposih' veintegers uith max[i, y)=n, then x=y.
ta'sftepiSupposethat 11= l.Ifmi'i^yjMandiandyarepositiveintegerSjWehave^ iandy= 1.
JnWwStep: Let it be a positive integer. Assume that whenever maxfy y) 4 and1and y are positive integers, then1-y. Now let maxC^ y):it+1, where1and y areposih'veintegers. Then masOc -1, y -1)=it; so by the inductive hypothesis,x-1=y -1. Itfolks thatx=y,complehhgtheinductivestep.
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