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Question: problem 6 what is wrong uith the following induction proof...

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PROBLEM 6. What is wrong uith the following induction proof that all elements x1, ,xn in a set of n elements are all equal? Basis step (n-1): The set has only one element which is equal to itself Inductive Hypothesis: Assu ... ,^n of any n-element set are equal (n > 0). Inductive Step: Suppose that {x1,x2, ,zn,2n+1} İs a set of n+1 elements. Now {x1,x2, . . . ,xn) is an n-element set, so by the inductive hypothesis x1 = x2 = me that all elements ri, = xn. Similarly, {T2, ,en,en+1} įs an n-element set, so by the inductive hypothesis x2 = x3 = . . . = xn+1. Therefore x1 = x2 = .. . = xn+1.

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