<p>Can someone explain the problem in this inductive proof? thanks!!!</p>
<p>This arguemnt shows that all people have the same height. More formally, it is shown that if X is any set of people then each person in X has the same height as every person in X. The proof is by induction on n= the number of people in X.
Base case n=1. This is clear, since if the set X contains just one person then that person certainly has the same heihgt as him/herself. </p>
<p>Induction step. We assume that the result is true for every set of K people (induction hypohtesis), and deduce that it is true for any set X containing exactly K+1 people. </p>
<p>Let X contain exactly k+1 people. Coose any person in X, and let Y be the set X with a removed. Then Y contains exactly K people who, by the induction hyptohesis, must all be the same height: h meters, say. Choose any other person b in X, and let Z be the set X with b removed. Since Z has just K people, the induction hypothesis applies, to give that the people in Z all have the same height- let us say j meters. Now let C be any person in X other than A or B. Since b and C both in Y, each is h meters tall. Since a and c both are in Z, each is j meters tall. So h =j. But htis means that a and B are of hte same height. </p>
<p>Thus, this has been proven by induction.</p>