Question

What is wrong with this "proof"?"Theorem" For every positive integern, ifxandyare positive integers with max(x, y) =n,thenx=y.Basis Step: Suppose thatn= 1. If max(x, y) = 1 andxandyare positive integers, we havex= 1 andy= 1.Inductive Step: Letkbe a positive integer. Assume that whenever max(x, y) =kandxandyare positive integers, thenx=y. Now let max(x, y) =k+ 1, wherexandyare positiveintegers. Then max(x−1, y−1) =k, so by the inductive hypothesis,x−1 =y−1. Itfollows thatx=y, completing the inductive step.

Answer 1

Every step is wrong in the proof theorem

Explanation:

The inductive step : whenever max(x, y) = k and x and y are positive integers, then x = y. is wrong because

If max (x,y ) = k + 1 then max ( x-1, y-1 ) = k

and by inductive hypothesis : x-1 = y-1 and x =y

example :

max ( 2, 3 ) = 3 where x = 2 , y =3

and x ≠ y hence the inductive step is wrong