At the end of 2008 the College Mathematics Journal will stop running its 20-year column “Fallacies, Flaws, and Flimflam.” The column was devoted to “mistakes, fallacies, howlers, anomalies, and the like”—usually found on student work. In honor of the departure of this entertaining column I submit the following FFF which was submitted as a solution to a homework problem in my Discrete Mathematics class.
Prove or disprove: the quotient of any two rational numbers is rational.
False. We will present a counterexample. The numbers 22 and 7 are rational. However and is irrational. Thus the conjecture is false.