Posted by: **Dave Richeson** | December 18, 2008

## Fallacies, Flaws, and Flimflam it’s been good to know ya

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.

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I can beat that with a submission from my geometry class. I forget what the theorem was the student was proving, but the first line was: “We will begin by assuming the conclusion.”

By:

Robert Talberton December 18, 2008at 10:54 am

Excellent! At least (s)he was being clear about her/his assumptions!

By:

Dave Richesonon December 18, 2008at 11:14 am

22/7 and pi are extremely close, but they are not equal.

By:

Stephenon February 22, 2012at 7:12 pm

Exactly. That’s what makes this funny. :-)

By:

Dave Richesonon February 22, 2012at 8:33 pm

However, perhaps the student was right —> 1/0 is not a rational number. So there is a counterexample that shows the statement is false.

By:

Stevenon January 30, 2013at 1:32 am

Exactly—it is false, and that was the counterexample I was looking for.

By:

Dave Richesonon January 30, 2013at 10:36 am