It has been a general trend in the teaching of mathematics that one should not show the students what could go wrong, if some necessary assumption was missing, ”because the students would be bewildered”! However, not all mathematicians agreed in this viewpoint, including the author of this book. To their philosophy counterexamples should guide the reader towards a better understanding of the underlying theory.
Some mathematicians including the author of this book believe that counterexamples will guide the reader towards a better understanding of the underlying theory.