Here is a proof that all human beings have the same age Wher

Here is a \'proof\' that all human beings have the same age. Where is the flaw in the argument? Proof. (Base case n = 1) In a set with only 1 person, all the people in the set have the same age. (Inductive hypothesis) Suppose that for some integer n greaterthanorequalto 1 and for all sets with n people, it is true that all of the people in the set have the same age. (Inductive step) Let A be a set with n + 1 people, say A = {a_1, ..., a_n, A\" = {a_2, ..., a_n + 1}. The inductive hypothesis tells us that all the people in A\' have the same age and all the people in A\" have the same age. Since belongs to both sets, then all the people in A have the same age as a_2. We conclude that all the people in A have the same age. (Conclusion) By induction, the claim holds for all n greaterthanorequalto 1.

Solution

The proof fails in the inductive step

BEcause when n=2 the proof does not work.

Because then n-1=1 and n=1 is true but does not imply n=2 case is true.