Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition and facile reasoning can often be misleading. However, errors can slip past the most watchful eye, they are often subtle and difficult to detect; but when found they can teach us a lot and can present a real challenge to straighten out. This book collects together a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves. Each of these items is carefully analysed and the source of the error is exposed. All serious students of mathematics will find this book both enlightening and entertaining.The men are given the following instructions: aquot;You are not allowed to discuss the color of your hats. ... An induction argument can be used to show that once the guest has made her announcement, all individuals with red hats will ... A version of this puzzle appears in Michael Spivak, Calculus (second edition) Publish or Perish, Inc., page 35, problems 27 and 28. ... I am indebted to a reviewer for directing my attention to the charming childrena#39;s book, Annoa#39;s hat tricks, by Akihiro Nozakianbsp;...
|Title||:||Mathematical Fallacies, Flaws, and Flimflam|
|Publisher||:||MAA - 2000-06-15|